The name is simply a description. The minister-y west of London. Thats all it means.
Westinster includes the "abby" which is a monastery , and the the "Royal Peculiar" which is the church.
This is where the Westminster confession was drawn up.
There was an Eastminster, near the tower of London.
A church that adopts that name usually associates themselves with the said same confessions
Hope that helps.