Westminster is a town on the Thames River, just west of London. The name West Minster dates at least from 875 AD in a charter of King Offa. Since Malory uses the name, it seems more than fair for us to use it.
The monastery was built on Thornea, a small island formed by outlets of the Tyburn and a ditch. The Thames was the eastern boundary. The monastery already existed at the time of the charter (perhaps on an old Pagan holy site?).
Canute or a predecessor established a royal palace here, and Edward the Confessor built a new church and monastery. The town grew up around the religious establishments. In Arthur's England, London would not yet have engulfed Westminster.