In Voyager, he’s shown to have pips. In fact, switching him over to Command mode shows a deliberate animation of pips showing up on hid collar.

However, it is possible that this is something that only applied on the Voyager thanks to their excsptional circumstances, and regular Starfleet doesn’t recognise it as a “proper” rank.

• Can a self-aware hologram hold rank or a non-com position in Starfleet?

Technically, yes, in practice, it would be a bit more complicated. A lot of the Federation still has issues around recognising the personhood of inorganics, and a good many of them would hold the early Voyager attitude of seeing him as a regular hologram/tool that the Voyager got too attached to, like the Enterprise did with their Data.

• If so, how would the Doctor attaib it?

The regular way, in theory. The ranking system technically doesn’t change depending on what species you are, other than some minor twiddling to account for your species’ characteristics.

It would be silly to expect a species who can’t speak to give verbal commands, for example, or give them a crew who is not receptive to telepathy.

In practice, there’s a lot more complications, like how the crew of the Sutherland nearly mutinied against Data because they believed him to be a dispassionate computer weighing lives at data points.