An Imp is born already knowing its name and that of its master, since, after all, both names must have been uttered and repeated over the course of the nineteen-moon-cycle ritual required to create the Imp in the first place. As such, an Imp name is technically just words of magic strung together, as part of an incantation. It’s quite possible, then, for two Imps to share the same name if the same words were invoked in their respective creations, but given the vast lexicon of dwimmercraft, that seems highly unlikely.
Because an Imp’s name is so embedded into its psyche, the mere utterance by the Imp’s master will send a deep fear into the Imp’s heart. The Imp will drop whatever it’s doing and heed its master’s call; or so that’s the intention of the spell. Imp incantations have been known to wear off over time (centuries), so it is best to renew the spell every few hundred years or so, which is a massive undertaking in itself, and likely not worth the effort. This is the main reason why Imps get transferred from master to master.