^Going by Mike Sussman's Archer bio, it appears the Imperial Guard was renamed simply the Andorian Guard after the UFP was founded. Which makes sense, since it wasn't part of an empire anymore.
Well, Andor: Paradigm
established that the Imperial Guard still existed in 2376 -- though, of course, that was 215 years after the founding of the Federation, so there was plenty of time for a name reversion.
And it's questionable how much of an empire Andor's was in any but the most ceremonial, in-name-only sense of the word. Andor: Paradigm
established that Andor had been united under a single constitutional monarchy whose throne legally still existed but was left deliberately empty (with the Parliament Andoria and Presider governing in the Empty Throne's name), and there's no indication of any conquered populations prior to the founding of the Federation -- the Andorians didn't even govern the Aenar on their own world, according to ENT's "The Aenar." So I can easily see the Andorian polity's name staying "Andorian Empire" even during Federation Membership, since it seems to be an empire in name only.