You don't need to go to the DMG, the PBH has you covered:
p174: Sometimes, the DM might ask for an ability check using a specific skill - for example, "Make a Wisdom (Perception) check." At other times, a player might ask the DM if proficiency in a particular skill applies to a check.
So yeah, by RAW it needs to specified prior to rolling, either by DM fiat or player request. I don't see any issues with a veteran group managing on player good faith though, that method might have some tangible benefits as far as immersion and narrative flow goes.