I did some rudimentary searches on the Collins name, and it is common in England, Ireland and Wales. I would tend to suspect this family is English as in 1795, Barnabas moving to England is considered a good cover story, in 1897 Quentin implies he has visited family in England, and in 1967, Elizabeth says, "I didn't know we still had family in England."
The name Collins derives from two sources, in England it was diminutive for Nicholas; in Welsh-Gaelic, it means roughly "darling", but usually in reference to small animals, most especially puppies or small dogs. (Welsh sp. cuilein)
Maybe this explains Barnabas's puppy eyes.
Michael
PS I did a scan for "Barnabas Collins" and a few real people came up on some geneaology sites, but it was a kind of a ruse to lead me to signing up for "Ancestry.com". My own family history book lists an old will circa 1690s in which a family member bequeaths some furniture to, (and I kid you not, this is TRUE) to his "cousin Barnabas Joyner in England!"