The original name for audio cassettes was Compact Cassette, which presumably inspired Compact Disc. But that moniker was long forgotten by the time CDs came out (although its logo probably still appeared on some cassette shells).
I always considered "Compact Disc" to be a dumb name; but I suppose it was forgivable as a reference to the much larger LaserDisc.
I always assumed it was a reference to music vinyl records. (Same size as LaserDisc.)
Per the Wikipedia article on Compact Disc:
"The compact disc is an evolution of LaserDisc technology, where a focused laser beam is used that enables the high information density required for high-quality digital audio signals."