Bcmdmmsg.exe
(Broadcom)
Broadcom Modem Messaging. Background task installed with the drivers for "BCM V.90 Modems". Broadcom modems are OEM modems which other companies put their names to (e.g. "Gateway").
Recommendation :
Broadcom modems are almost always 100% software controlled modems. Thus, while we are not totally sure about the role of BCMDMMSG, it is highly likely that this background task is essential to the proper functioning of your modem leave alone.