Complex sentence: The trio accepted the name for its "psychedelic ring" and ambiguity, but by then they had already been together for at least three months (five rehearsal sessions and one live show) without one.
Split into simpler sentences: The trio accepted the name for its "psychedelic ring" and ambiguity. By the time the group took a name, they had been together for at least three months (five rehearsal sessions and one live show) without one.