canada, (and i know this for a fact cause im in the canadian army) has used the rank of Commodore sense it has separated from UK in the 70's. in the 90's the term/rank of commodore in all of canada was lost from its insignia book indicating that canada no longer has used the rank.
there however in our history is showing that anyone to which carried the rank had been swapped over a Rear Admiral's, and for the part seen them as Rear Admiral lower halfs.
US History/Insignia book, to which Canadian Personnel should and have also been trained in shows that the same thing. however there is no date to when US may have changed.
UK history still has it in they books, but it also has been noted that by other nations they are to be referred to as Rear Admirals.
so the given rank of Commodore has been, and is now promptly considered history, and has be combined into Rear Admirals. there are 2 Grades to Rear Admirals. both lower and upper. upper being highest, and neither of them meaning a dam thing, cause a admiral is a admiral.
I do remember one episode now that you said something, it was in TOS onboard the Enterprise, where they had spoken to a Commodore. so i retract my statement there.
Commandant. as you may or may not be aware. the position of commandant, the person in said person was always called commandant John Doe, or Commandant Jane Doe. indicating it, to be a form or rank or other. you dont see people going around saying Police Officer John Doe, you see them calling them Cst. John Doe. giving rank to the person.
you are right thou, there is no prove that SF had gone away with commodore. but given the history to which is presented, Rear Admiral never existed with the rank of commodore. and thou i like the sound of Commodore, does it really matter if we strip the two of these ranks to best suit you and maybe 100 other people?
The rank is still very much in use in the Canadian Navy (for evidence, I will note to you that the current commander of the Naval Reserve is Commodore David Craig).
There was an extensive and arcane reason for the dropping of Commodore from the US Navy, having something to do with payscales. I'd have to look it up to be sure I explained it correctly, but the end result is that the old one star rank of Commodore is no longer used, and has been replaced by Rear Admiral Lower Half. Admirals holding this rank actually still wear two stars.
In Starfleet, there were several Commodores, as has been pointed out.
Commandant is a position, denoting an officer in a command position, usually at a training facility, such as the Academy. The Commandant could be any sort of senior rank, but is usually an Admiral or General of some variety. The term is also used as a rank in some non-english speaking nations. You would call him or her "Commandant Smith," just as you would say "Doctor Smith."
Oh, and for the record, I did my service in the Canadian Navy (though I didn't rise anywhere near as high as Commodore!).