Yep, anyone requesting one can pay the FCC a bit more for a vanity call sign. There are similar rules for amateur radio operators.

In NYC, where most of the national radio and TV networks originated, their call signs reflect the original broadcasters. WCBS = Columbia Broadcasting Service. WABC = American Broadcasting Company [[it's original callsign was randomly assigned WJZ) WNBC = National Broadcasting Company.

As others have posted, the local network operators often would ask for a callsign reflecting the name of the company that ran the affiliate.