EXT. SPACE - RUNABOUT (OPTICAL): coming out of the other side of the wormhole... which disappears behind them...
INT. RUNABOUT (OPTICAL):
SISKO: Can you get a fix on our coordinates... ?
DAX: (checking) There's a star just under five light years away... no M class planets... Computer, identify closest star system...
COMPUTER VOICE: Idran... a ternary system consisting of a central supergiant and twin O- type companions...
SISKO: (reacts) Idran... that can't be right...
DAX: Computer, basis of identification...
COMPUTER VOICE: Identification of Idran is based on the hydrogen-alpha spectral analysis conducted in the twenty-second century by the Quadros-One probe of the Gamma Quadrant.
SISKO: (stunned) The Gamma Quadrant. Seventy thousand light years from Bajor? I'd say we just found our way into a wormhole...
Realism: If I recall correctly, there are roughly one hundred billion stars in our galaxy. In any case, even if this figure were a million times too large, it would be exceedingly unlikely for every star system in the galaxy (including parts which no starship has visited) to have been given a nice-sounding name (as opposed to a cryptic alphanumeric code), never mind for Starfleet officers to have memorized them all and be able to recognize them upon hearing the name.
It's pretty difficult to think of a way to rationalize this particular error, although you are, of course, welcome to try.
Your reasoning is, of course, correct. The only way I see that Sisco could know the name of the system is if its part of some popular "legend" or "old sailor story". My guess is that sometime in the past a Federation ship (or one from the Alpha quadrent) got sucked through the wormhole and mapped the system, but when it returned the computer that stored the course they took was damaged. The crew then told the tale of how they got sucked to the other side of the galaxy, and somewhere along the way (before the name of the system was logged into federation computers) a name, Idran, was attached to it.
Devolution is quite as natural as evolution, and may be just as pleasing, or even a good deal more pleasing, to God. If the average man is made in God's image, then a man such as Beethoven or Aristotle is plainly superior to God, and so God may be jealous of him, and eager to see his superiority perish with his bodily frame.
-H.L. Mencken