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.