St Thomas is one of the roads on the Bishopdown Farm estate which has been named in honour of a saint, or in this case in honour of one of a number of possible Saints.
Wikipedia lists 20 Saint Thomases 1 (according to the Spectator2, the plural of Thomas is indeed Thomases – if Boris Johnson says so, it must be right).
I have written about Thomas A Becket in the entry on St Thomas’s Square SP1. The other famous St Thomases, most likely to have been in the minds of the people that named St Thomas Close, would probably be:
[...] roads in the ‘Bishopdown Farm’ estate are named after individual saints (for example St Thomas Way or St Clements Way) or after some other religious concepts (e.g. Apostle Way, The [...]