Never. All the tandem signatures I've seen feature the girls' full names:

And I've been wondering about that very fact lately. It seems odd that the notion of OTMA is so ingrained in Romanov culture and yet in all my thousands of scans and photo albums, I don't have a single example of an OTMA signature. As best I can tell, the original source for the "OTMA" acronym was Gilliard. He had this to say:
"With the initials of their Christian names they had formed a composite Christian name, Otma, and under this common signature they frequently gave their presents or sent letters written by one of them on behalf of all."I don't find it hard to believe that the girls might have used their initials as a form of shorthand from time to time. It seemed a fairly common practice in the IF -- the empress's diaries and letters are filled with initials, for example. What I've come to question recently is whether Gilliard overstated things when he claimed that Otma was a "composite Christian name" used by the GDss to refer to themselves as a clump, as opposed to a simple abbreviation.
I have seen a photo of a poem by Petrov dedicated to "O.T.M.A." but even that is clearly an abbreviation rather than the name-like "Otma" of Gilliard's claim. (I'd post a scan, but I can't get one without utterly destroying the paperback book it appears in.) Further, I don't recall ever seeing "OTMA" or "Otma" in any of the IF's diaries or letters. Instead, it's "we," "we four," "the girls," or "the sisters."