So I tried the rename command:
hg rename OldFileName.ext NewFileName.extbut got the response:
not overwriting - file existshg status reported that nothing had changed. Googling showed that you need to use the –after option, to specify that you don’t actually want Hg to move the file in your working copy, just track that is has moved.
hg rename --after OldFileName.ext NewFileName.ext
I think the same should work for Move too.