There seems to be no logical difference between the "Fixed Doh" (which was probably the original form) and the use of note letters (C,D,E...).

It was originally invented by a monk as a mnemonic system "Ut Reh Mi..." from the first words of a hymn in which the start was an ascending scale, but Doh is easier to sing then Ut.

The movable Doh IS different and more flexible, of course.

PS
I believe that the Beatles wrote one song in Locrian mode.