It is illegal to register or use a dba company name that could be easily confused with another company in the same business.
The FCC licensed WABD (which IMHO is too close to WABB but that another tread). Being "licensed" by a branch of the Federal Government most likely trumps Alabama laws. In the MTM verses WKRP case the radio station "won" by basicly because their FCC Call letters were
WKRP. IIRC The TV folks eventually did make a set of jingles for WKRC Cincinnati. WKRP's Johnny Fever was really Bobby Harper at WQXI Atlanta. WQXI was a stop on WABB's former Scott Shannon path to Z100 where he "perfected"* CHR in NYC.
* Perfected" is probably the wrong word but worst to first in market #1 does make station owners happy.