The Greek gods have a Roman aspect in which their personalities and sometimes attributes change. These personas are still honored in modern times at Camp Jupiter. This camp normally uses their Roman names instead of their Greek ones. In their Roman forms they tend to be more disiciplined, militaristic, warlike, and more united.
Even though Roman demigods only use the Roman names of gods, Titans, and monsters, when Jason Grace was talking about the assault he led on Mount Orthys, he used the Greek names for Kronos (Saturn) and Krios (Crius), although this may be because he'd been staying with the Greek demigods for so long that he'd gotten used to saying the Greek names for the time.
The Roman form of a Greek drachma is an aureus, a gold coin weighing around 8 grams.
Many gods only have one form, like Terminus and Janus. Neither of whom have Greek forms.
It is unknown if gods can possibly be in their Greek aspect in one place and their Roman form in another place.