Oh yeah. It’s Irish, one of the many many orthographies of the word dubhainn: the dubh- root meaning “dark” or “black” or sometimes “shadowy”, and the “-ainn” suffix being sort of a diminutive, so that the name renders somewhat as “little dark one”.
What’s interesting is that most Americans pronounce it incorrectly (and for that matter, I was raised to pronounce it wrong too, and still do). doo-AYN or doo-WAYNE is wrong, as it turns out. In Ireland the name is pronounced DOO-uhn almost all of the time. What happened is that when the various waves of immigration headed for North America, the immigration authorities were quite arbitrary about what spelling they assigned to DOO-uhn when they heard it. You see Doone, Doane, Dunn, Dunne, Dewan, and God knows what else, and they all go back to dubhainn most of the time.
The side effects of this can be amusing. I once spent the guts of an afternoon in an airboat in the Everglades with Jimmy Doohan (secondary to a Star Trek cruise out of Miami) comparing geneaologies and discussing the possibility that we were somehow related, as “Doohan” is yet another of the ways that dubhainn got transcribed on entry. …But anyway, any pronunciation that puts the emphasis on the second syllable is usually a sign that the wearer’s family has been in North America for several generations.
…That may have been TMI. Anyway, now you know.