In reply to static266:
Not sure what 'evidence' you want. Basic google searches using the two spellings gives a reasonable idea of what the currently accepted spelling is (I found very few incidences of the Tregalen spelling)
The derivation of 'Cwm Tregalan' isn't clear - 'Tre(f)' refers to a settlement (but in this instance it could either be a settlement at the site, or that the grazing in the cwm belonged to a settlement elsewhere). 'Galan' could be a reference to the first day of the month ('Calan'), or more likely a corruption of 'Heart' ('Calon') or 'Holly' ('Celyn').
A few sources (other than 'Local Knowledge') in support of the 'Tregalan' spelling:
OS Mapping (various editions)
Harveys / BMC Mapping
Bartholemews mapping
Snowdonia National Park website (both languages)
Snowdonia society website (both languages)
Scrambles in Snowdonia (Ashton)
Visions of Snowdonia (Perrin)
Welsh 30000ft Challenges (Clayton and Turnbull)
Rock Trails Snowdonia (Gannon)
V12 blog
Welsh Peaks (Poucher) and Tremadog (Long) both seem to avoid referring to a specific name for the upper part of Cwm (y) Llan.
Post edited at 00:30