The FCC does not do any kind of registration of call signs for consumer devices or college campus radio systems operating under Part 15 of the FCC Rules.
As far as Part 15 device operators using call signs, the FCC provides guidance in ยง73.3550(l) of the rules:
Users of nonlicensed, low-power devices operating under Part 15 of this chapter may use whatever identification is currently desired, so long propriety is observed and no confusion results with a station for which the FCC issues a license.
If you want to see which call signs are currently unused, visit:
https://recnet.net/calls
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