The Arizal used to tell people who they were in previous lives. The Baba Sali (according to his biography) asked another kabbalist whose neshama he had, and after “looking into it” the rav said it he had Chizkiyahu’s. But I’m not aware of rabbonim who do this now or say we should go to non-Jews for this reason.
We believe in gilgulim so in terms of hashkafa it might not be a problem if it’s done in a secular way (if that’s possible). But the potential to be confused or mislead or tricked by charlatans (or hypnotists who can get you to believe something is real when it’s not) is so big that it would seem to be a really bad idea. Perhaps if someone feels like they have a really good reason to they could get a heter from a Rav.