Options vary depending on the VHF. Some may ignore own MMSI, but others certainly do not. Some allow disabling the internal AIS receiver and using AIS data from
NMEA, others do not.
On some VHF models, the only option is to disconnect them from
NMEA and let them operate independent. If you want to use
DSC calling from the chartplotter, that won't
work.
Another "option" I have met a few sailors who thought seeing their own ship was normal, as they knew their AIS was transmitting. They had issues with AIS in the past and it gave them comfort. It bugged me, but they insisted I leave it as is.