No !! As far as I know, initially they were called as Basnyat. But later on because of easiness to pronounce they strated to call Basnet.

In Jumli Malla kingdom, Basnyat were authorized to settle new villages towards eastern part. If you see their population settlement you will not find them significantly in far western region. They migrated from west to east.

There is a famous saying about them,
NEPAL BASNYAT KO TALWAR RA PANDE KO DHAAL LE BANEKO HO !!!!