Generally…no. Pretty much all cell boosters will work with all carriers for improved voice coverage. If you have a 4G cell booster made before 2013 you may have bought one that only works with one carrier. The easiest way is to look at the model number. Generally 4G boosters for AT&T end in an “A” while those for Verizon end in a “V.” But the days of single-carrier data boosters came and went very quickly and today’s boosters use five bands to be able to cover all voice and all data for AT&T, Verizon, T-Mobile, and most other carriers.
The lone holdout, of course, is Sprint, which uses non-standard frequencies in many areas. But then again if you have Sprint, you probably weren’t using a data booster because as far as I know there was never a data booster made for their frequencies. If you’re switching from Sprint to another carrier it might make sense to look into a new 4G booster at the same time.