(this applies to animal species -- scientific names of plant species have slightly different rules -- SECTION 6.6).
Musca domestica is the name of a species.
1. Species names are binominal (i.e., consist of two words). The first word is the generic name. The second word has been called "specific name" or "specific epithet" -- but it is not the species name. Both words together are the species name.
2. Conventionally, the two words are underlined when handwritten or typed, to indicate to an editor or printing company that they should be italicised when they are printed on a printing press. One reason for putting them into italics is to indicate that they are not English -- they are Latin.
3. Unlike Spanish and many other modern languages, Latin is not written with diacritical marks ("accents"). Names of species have no diacritical marks and may not be hyphenated.
4. In headings, all letters of the species name may be capitalized.
In text, when there is a mixture of upper and lower case (large
and small letters), the following rules apply:
4a. The first letter of the first word (the generic name) is always
capitalized.
4b. The first letter of the second word is not capitalized for
the name of any animal (vertebrate or invertebrate).
5. No two species of animals may have the same species name. No one species of animal may have more than one valid species name. The scientific name of an animal species is intended to be unique, to be used worldwide by biologists and others, no matter what language they speak.
6. In all countries, a few of the most conspicuous and/or abundant animals have been given "common" names in the language of that country. Others have been given vernacular names. Would it not be simpler to use one 2-word scientific name worldwide for each animal species rather than deal with translation of each name into thousands of human languages? [SEE ALSO SECTION 8 and 14.b].
7. Many scientific journals require the name of the describer after the name of a species at first mention. This means you have to write "Musca domestica Linnaeus". This is because Linnaeus, otherwise known as Carl Linné, so sometimes written as Linné or "L.", described Musca domestica originally. He was the author of the species name.
8. What if the name of the describer has parentheses around it as in Creophilus maxillosus (Linnaeus)? It means that Linnaeus described that species originally, but as belonging to some genus other than Creophilus. In fact he called it Staphylinus maxillosus. The parentheses around his name acknowledge that he described it in some other genus, but that now it is called Creophilus maxillosus because someone later changed the generic assignment.
9. The editorial board of a scientific journal can decide whether it wants the name of a describer to be included (after a scientific name) as a general policy in anything published in that journal. But the presence or absence of parentheses is not subject to the whims of an editorial board -- nor to yours.