Because of his original purpose, it makes sense that the Doctor wouldn’t have held a Starfleet rank during Voyager.
However, in Prodigy, he still doesn’t have pips. This leads to my questions:
- Can a self-aware hologram hold rank or a non-com position in Starfleet?
- If so, how would the Doctor attaib it?
According to the STO wiki, he doesn’t wear them by choice but does have a rank. That might be a reasonable explanation; I can’t imagine Janeway not at least trying to field commission him.
Voyager's original CMO was a Lieutenant Commander, which is presumably pretty typical for a ship of Voyager's size. Bashir was commissioned as a Lieutenant Junior Grade to be the CMO on a backwater space station, so that's presumably the bare minimum.
I would expect the Doctor's first official rank (whatever that might be) to stick with him, plus promotion as appropriate. Adjusting it up and down based on posting would be a bizare thing to do for any other crewperson, and I'm sure The Doctor would object vigorously to such a thing.