There are BMPs, BMDs, and BTRs. If you're feeling fancy, you call their generation number (BMP-2, BTR-80). If you're an incessant pain in the ass, you call their model

Off the top of my head, the BRM was an earlier-model BMP-1 with additional radio and/or recon gear to support a field command role. Visually, the only difference I can think of is smallish optical mounts on the turret top, and the lack of an ATGM rail? So yeah, even if it was a BRM (which I'd imagine is an unlikely choice for the mission creator), it'd just confuse all the poor wickle squaddies hearing that rather than "BMP" :v