The plumbers here can often identify the manufacturer of old fixtures, but they usually need to see the "insides". A photo of the hot or cold side with the handle and decorative flange removed might be enough to give them a clue. Removal and photo of the stem assembly itself would be even better but requires the water to be shut off, and might not be a good idea if you're not somewhat "handy".
Old Retired Computer Programmer
Obsolete and loving it