Help with Old Town

[Mary Bright]

I need your consulting about the question how to use capitals with proper names correctly. If I have a sentence:
'Old Town is near the river. The T(t)own got its name due to an old legend... '.

So, what letter shall I use if a common noun which is part of a proper name is repeated, like in the example above?

[montfan]

* not a teacher

lowercase town.