Very good answer from ckersch - use that for your core information. But here’s a few additional ideas. This Wikipedia article has a list of useful words for making species names.
Here are some Real World rules on naming creatures after people or groups of people.
Traditionally, the genus part of scientific names of animals take the masculine form of the noun (ending in –us, Ursus, Equus, Tyrannosaurus) more often than they take the feminine form (ending in –a, Loxodonta, Giraffa, Maiasaura) or the neuter form (ending in –um, -e, -erum, Eledone). Confusingly, words ending in –is (Canis, Felis) are sometimes masculine sometimes feminine. If you want your world to be a bit different, then change that ratio by ‘feminising’ or ‘neutering’ the word: Equa instead of Equus, Ursum instead of Ursus.
You can use the same word for both the genus and species name. Examples include Meles meles (Eurasian badger), Vulpes vulpes (red fox) and Gorilla gorilla (western gorilla). This will usually be because the animal in question is the first one of its kind to be named. Sometimes simply because it was common in the land where the naming system was invented!
You can make compound names by using a common suffix which describes your animal. So, for instance teuthis means ‘squid’, while myrmex (Greek) and formica (Latin) both mean ‘ant’. Thus there are a whole slew of squid with names such as: Architeuthis, Magistoteuthis, Histoteuthis. And a whole bunch of ants called things like Teratomyrmex, Brachymyrmex, Iberoformica, Proformica and so on. This means that is if you have a group of animals in your world which are of one type – dragons, for instance – you can use one word to make your species more diverse. Draco = Latin for dragon, so...
Basilodraco volans – the king dragon which flies
Teratodraco siluriensis – the monster dragon from the land of the Silures (a bit of Wales)
Place names can end in –ensis or –iensis (Draco madagascariensis, Draco senegalensis, Draco canadensis) as well as the traditional –us or –a endings (Draco tibetanus, Draco americana).
If you want to name bigger groups of creatures you can use family names. A family is a higher taxonomic grouping which includes all the species of that sort. Animal family names end in –idae and plant family names end in –aceae. For instance, Canidae (the canine family - dogs, foxes and wolves), Felidae (cats), Formicidae (ants), Rosaceae (rose family), Brassicaceae (cabbage family). You do not italicise family names.