To be honest I am not sure there is a better answer to this then the following excerpt:

From the following Walter Thornbury, 'Westminster: Introduction', in Old and New London: Volume 3 (London, 1878), pp. 5-10 http://www.british-history.ac.uk/old-new-london/vol3/pp5-10 [accessed 14 March 2015].

the origin of the name of Westminster is clear to the veriest child in such matters. The city must have taken its name from the noble Abbey Church of St. Peter's, the "Minster" in the "West," as doubtless it was called by the citizens of London in the days when London ended at the gate of "Lud," or, at the farthest, at Temple Bar. Stow tells us that it obtained this name all the more easily as "there was another Minster eastward of the City, and not far from the Tower, called 'Eastminster;" but the honest old annalist has forgotten to tell us where it stood precisely, though a modern writer places it on Tower Hill. For ourselves we can only say that we have not been able to verify the assertion.

This is a fun little read too, nifty place

http://www.bbc.co.uk/history/trail/church_state/westminster_palace/change_palace_westmin_01.shtml