“Traditionally” is a problematic word when it comes to romanization in Taiwan, especially for places that aren’t on lists of official place names.
Hanyu Pinyin: Tianmu (current official system in Taipei, which Tianmu belongs to)
Tongyong Pinyin: Tianmu
MPS2: Tianmu (Taiwan’s official system from 1986 until the adoption of Tongyong)
Wade-Giles: T`ien-mu (but often spelled – incorrectly – in bastardized form: Tienmu) (Wade-Giles was never Taiwan’s official romanization system.)
Gwoyeu Romatzyh: Tianmuu (Taiwan’s official romanization system until 1986.)
Until about five years ago or so, the form most commonly seen was probably “Tienmu,” which, as I noted above, is incorrect in all major romanization systems.
It was not separated into two words. (It isn’t two words.)
“Mu” did not and should not appear in upper case.