I know it's not stated verbally, but IIRC, Fletcher's rank designs included one for Commodore, which I believe was worn by some background characters in the later TOS movies.
Although Starfleet *may* have phased out the Commodore rank, we really have no evidence that it uses the terrible-sounding "Rear Admiral, Lower Half". I believe the only "one-pip" admiral we ever saw on-screen was Admiral Quinn, and even that's not definite, since they were using a different rank insignia for admirals in TNG season one.
(Assuming Quinn is a one-pip admiral, then we would know that they are called admirals, rather than commodores, by the TNG era. My own personal rationalization is that Starfleet changed Commodore to Commodore Admiral, which was an actual US naval rank for a whole eleven months. This would still allow them to be called "admiral", but also allows for the multiple references to "commodore" in Peter David's novels!
But you could just as easily say that Starfleet has commodores in TNG, and we just never saw any.)
And to Christopher's point about Kirk, based on Kirk's insignia, he would have been a Rear Admiral, Upper Half anyway, so he still would have skipped over the previous grade, whether it was called Commodore or Rear Admiral, Lower Half at the time.
Although Starfleet *may* have phased out the Commodore rank, we really have no evidence that it uses the terrible-sounding "Rear Admiral, Lower Half". I believe the only "one-pip" admiral we ever saw on-screen was Admiral Quinn, and even that's not definite, since they were using a different rank insignia for admirals in TNG season one.
(Assuming Quinn is a one-pip admiral, then we would know that they are called admirals, rather than commodores, by the TNG era. My own personal rationalization is that Starfleet changed Commodore to Commodore Admiral, which was an actual US naval rank for a whole eleven months. This would still allow them to be called "admiral", but also allows for the multiple references to "commodore" in Peter David's novels!

And to Christopher's point about Kirk, based on Kirk's insignia, he would have been a Rear Admiral, Upper Half anyway, so he still would have skipped over the previous grade, whether it was called Commodore or Rear Admiral, Lower Half at the time.