If you want to become a taxonomist, you need to learn the basics of Latin grammar, and for this you would do best to take formal courses in Latin. You also need to study several editions of the International Code of Zoological nomenclature (ICZN 1964, 1985, 1999) and understand how the rules changed from edition to edition.

When you have studied Latin you will understand that Latin nouns, adjectives, and participles have gender [masculine, feminine, and neuter] and are grouped into declensions with varying terminations (to indicate the 6 cases in the singular and 6 in the plural), and that adjectives and participles must agree in gender with the nouns that they qualify. If, now, you want to honor someone by naming a new species for him/her (this assumes the person is still living), or name a species after him/her (this assumes that the person is dead), then the following notes about creation of patronyms apply. A patronym is a scientific name created to honor a person [contrast with a toponym which names a species for a place]. Here, it applies only to the creation of species names.

These notes were written to aid Dr Khuong Nguyen (nematologist, Entomology & Nematology Department, UF) in selecting appropriate patronyms and is so reflected by examples below. His wife's name is Sam. The notes are based on ICZN. His name is masculine, hers is feminine, and these things are important in Latin grammar.

Names of genera of animals and plants are nouns in the singular and have gender [are either masculine or feminine or neuter]. You [the taxonomist] must determine [find out from previous usage] the gender of a generic name within which you want to create a new species-group name. A species-group name is the 2nd word in the name of a species (a binomen) or the 3rd in the name of a subspecies (a trinomen).

GENERAL RULE: Article 31 (a): A species-group name formed from a personal name may be either a noun in the genitive case [1], a noun in apposition [2], or an adjective [3] or participle [4].

[1] Article 31 (a) (ii): A species-group name, if a noun in the genitive case formed directly from a modern personal name, is to be formed by adding to the stem [*] of that name -i if the personal name is that of a man, -orum if of men or of man (men) and woman (women) together, -ae if of a woman, and -arum if of women.
Examples: Steinernema nguyeni (named for Khuong)
Xenorhabdus nguyeni (named for Khuong)
Paramecium nguyeni (named for Khuong)
Steinernema nguyenae (named for Sam)
Xenorhabdus nguyenae (named for Sam)
Paramecium nguyenae (named for Sam)
Steinernema nguyenorum (named for Khuong and Sam)
Steinernema nguyenarum (for Sam and her daughter)

[*] Many modern names do not have a stem (as defined in Latin), but a few men's names (e.g., Augustus, Julius) and many women's names (e.g., Alberta, Cristina, Helena, Julia, Maria, Roberta, Susana, Victoria, etc.) are in Latin form and so are treated as if the stem were August-, Juli-, Albert-, Cristin-, Helen-, Juli-, Mari-, Robert-, Susan-, Victori-, to which the genitive termination -i (for men) or -ae (for women) is added (augusti, julii, albertae, cristinae, helenae, juliae, mariae, robertae, susanae, victoriae). Some modern family-names (e.g., Parelius) that appear to be Latin may be treated as if they were Latin (with stem Pareli-, giving parelii in the genitive) OR as if they are not Latin and have no such stem (giving pareliusi in the genitive).

Note: there are other ways that the genitive case of nouns CAN be formed [in all 5 Latin declensions of nouns], but ICZN accepts only the method shown [in 1] above in which names of women are all assumed to be first declension feminine nouns, and names of men are all assumed to be 2nd declension masculine nouns.

[2] Recommendation 31A: An author who establishes a new species-group name based on a personal name should preferably form the name in the genitive case and not as a noun in apposition in order to avoid the appearance that the species-group name is a citation of the authorship of the generic name.
Example: Steinernema nguyen is not recommended

[3] Appendix D III: Such a name may also be formed by adding the adjectival ending -ianus, -iana, -ianum to the entire name [according to whether the generic name is masculine, feminine, or neuter], but it is better to use the genitive singular [formed from the personal name, as in [1] above].
Examples: Steinernema nguyeniana is not recommended
Xenorhabdus nguyenianus is not recommended
Paramecium nguyenianum is not recommended
[these adjectives must agree in gender with the generic name - regardless of whether they are named for Khuong or Sam]

[4] There seems to be no recommendation against using a participle, but it is very unusual (such a form is much more common as a toponym than as a patronym) and would be poorly understood, so best avoid it. Such names are formed by adding the genitive terminations -ensis, -ensis, or -ense to the stem of the name (or to the entire name if there is no recognizable Latin stem) according to whether the generic name is masculine, feminine, or neuter.
Example: Steinernema nguyenensis (generic name is feminine)
Xenorhabdus nguyenensis (generic name is masculine)
Paramecium nguyenense (generic name is neuter)
[these participles, in the genitive case, must agree in gender with the generic name - regardless of whether they are named for Khuong or Sam]

Potential problems: The rules and recommendations listed above are clear enough, but article 31 (a)(i) complicates the issue. It states: "A species-group name, if a noun in the genitive case formed from a personal name that is Latin, or from a modern personal name that is or has been Latinized, is to be formed in accordance with the rules of Latin grammar.
As above, we must assume that the expression "personal name" can be a first-name (e.g., John) or a family-name (e.g., Smith), which are neither Latin nor Latinized.
But if the first-name is a name from classical Latin (other than women's names in the first declension or men's names in the second declension), then the genitive case has a termination other than shown in [1] above. For example, the name Aeneas (genitive Aeneae)(but not Andreas, which is not classical Latin so does not form a genitive Andreae) is masculine, first declension, the names Hector, Hercules (but not Hercule or Herculeo, which are not Latin) and Pericles (genitive Hectoris, Herculis and Periclis respectively) are masculine, 4th declension nouns (adopted from Greek).It thus seems that we may elect to treat such names as either Latin or as being in a modern language. If we choose to treat them as modern names, then the genitive cases from which we form patronyms are respectively aenei, hectori, herculi, and pericli (following item [1] above). But, if we treat them as classical Latin names, then the genitive cases are respectively aeneae, hectoris, herculis, and periclis following rules of Latin grammar. Your simplest solution (if you do not want to be bothered with Latin grammatical usage of classical Latin names) is to follow the rules in item [1] above. As for names of women ending in -a (the typical Latin form) there is no such problem because the patronyms (?matronyms) terminate in -ae added to the stem no matter whether the names are treated as Latin or modern. Women's names Beatrix and Victorix (which would form the genitive as Beatricis and Victoricis) do not seem to be classical Latin, so the rules in [1] above can be followed.
We now come to family-names that "have been Latinized." In the early days (18th century) of taxonomy, when entire texts were written in Latin, authors had to write their names at least in nominative and genitive cases in Latin (and possibly also in accusative, dative, and ablative). Thus, von Linné became Linnaeus (genitive Linnaei), a second declension masculine noun, but Poda was Latinized as a first declension masculine name (genitive Podae). Such Latinization became less and less common through the 19th century and disappeared sometime in the 20th. The recommendation here is to avoid any new Latinization of such family-names. In other words, use the method described in [1] above. For example, if you want to form a masculine patronym from the family-name Smetana, form the genitive as Smetanai following item [1] above and do not Latinize the name as a first declension masculine name which would give the genitive Smetanae for masculine as well as feminine. For another example, if you want to form a patronym from the family name Smith, form the genitive as Smithi as in [1] above, and do not Latinize the name to Smithius which would give the genitive Smithii.
Finally, we come to family-names that appear to be Latin because they end in -ius [but, in fact, are not Latin]. These names, such as Fabricius and Parelius, are mainly from the Baltic. They are no problem. The family name of Johan Christian Fabricius (1745-1808) has always been treated by biologists as a Latin name, with genitive Fabricii. Modern names of this form may be treated as non-Latin (genitive Pareliusi for a man and Pareliusae for a woman) as in [1] above) or as Latin second declension for a man (genitive Parelii) or first declension (genitive Pareliae) for a woman.

Summary: use the genitive case as shown in [1] above, and forget about nouns in apposition [2], adjectives [3], and participles [4]. Do not Latinize names of people whom you want to honor by patronyms - simply use the method of forming patronyms as shown in [1] above.

Bibliography: The International Code of Zoological Nomenclature 1985 (third edition) and 1999 (fourth edition) [note that article 31 (a) (3rd edn) is called 31.1 (4th edn), that 31 (a) (i) 3rd edn) is called 31.1.1 (4th edn), and 31 (a) (ii) (3rd edn) is called 31.1.2 (4th edn)] and Latin grammars.