re knowing the names of tunes - no, I usually don't because the lead musician (Richard) in the folk band I was in until 2005 never thought it necessary to tell the rest of us! All we ever needed to know was the key or keys that the piece or set was/were in. The moment he'd start, it was instant recognition. Because I'd been in another band in the late 19770s, where the leader did name the tunes, I would sometimes ask Richard if we ever played (say) The Full Rigged Ship and he'd tell me we'd already played it that evening.
With songs it's totally different - I can instantly remember the tune and the words if someone requests a particular song. The chords just fall into place.