I agree that if nothing else, it would be beneficial to others to atleast (when appropriate) identify your own pet's scientific name so that we might slooooowly learn some more scientific names of the snakes we personally do not have/have in our area.
As to whether they're italicized, or in brackets or whatever, it doesn't really matter, but it is good practice. Italics can help readers subconsciously skip over the scientific part too, if they choose to 'read around it'.
After much hesitation and mind-changing, I have finally determined that my snaky must be a 'Maritime Garter' (thamnophis sirtalis pallidulus) .