But commander sounds too military and might give the Aliens the idea that Enterprise's visit could potentially be threatening.

I think they already knew that any Federation starship represented at least a potential threat.

Maybe since Counsellor is her primary function she identifies as such in Starfleet that may rank her as Lt. Commander but it is a thing she rarely uses.Same applies to Crusher she identifies herself as Chief Medical Officer or just doctor while she rarely uses her Starfleet rank which was commander(I believe).

Come to think of it, all those other officers, except for the captain and number one, seemed to have other qualifications, like doctor, science officer, engineer, counsellor, etc..

Actually, it seems that Dr Crusher never went to the Academy. In one episode she mentions that she was in medical school when she started going with Jack Crusher and then got married. It's quite possible that Troi didn't go to the Academy either. So in technical terms, it's probable that Dr Crusher and Counsellor Troi could not have achieved any command rank, even if they passed the "engineering test" where you have to pretend to holo-order your holo-friend to their holo-death in the holo-deck to save the holo-ship.

Beverly had that rank she took over as captain in the two parter Descent and she talks about passing the test Troi had to do and meeting friends from the academy passing all kinds of training and courses.So she probably had like basic Starfleet training much like in the army and you are then send to your specialisation like medic scientist engineer etc.

Maybe so. But even to be an ensign would require however many years at the academy, AFTER medical school. And it wouldn't be necessary to be a ship's doctor. She probably didn't plan/expect/want to go into higher ranks or command. So why would she have done it? I dunno.

Is it really that important? She is doctor first like Troi is a counsellor first.

First, last, and only, really. At least on a ship. Beverly could take "command" of Starfleet Medical and I suppose Troi could take "command" of Starfleet... Counselling...… But the idea of them being able to command a starship even occasionally is just more claptrap. I suppose it was done to show some women in authority without having to pay more actors. But it would have made more sense to have some other female commanders, such as happened at the start of the TNG episode "Disaster." Just don't immediately kill them off, m'kay?

But that isn't relevant for the episode we were discussing but maybe they were trained to function as a back up commander we don't know because we don't know the Starfleet Academy curriculum.It would seem very strange that Picard/Kirk are so well versed in art and Literature or archeology or playing a classical instrument etc.

Well remember, they had plenty of spare time. Even if they don't show it in the show. Since it would actually take WEEKS to get from one planet to the next.

Well enough time to train and study won't you think?

"Holodeck" training is the future.

I hate the holodeck.

The new show takes place on the holodeck.