There are only 4 persons in the social security death index with the name. You might expect those could be husband and wife,but all 4 are from different states. As for "hundreds" in public records.. zabasearch is a fairly good directory, but it has 95, and many of those are obvious duplicates.
One thing that is always possible with a very rare name.. the ones you find, can be a spelling variation of another original name. Persons named Dolphay and persons named Dolfey ARE known to be related, but each took a variation of Dauphinais. Another possible reason is that it is a very recent immigration (ie grandparent), which, using records, you can find who is or isn't related. Perhaps your father can confirm when his (father/grandfather) came to the US. Or, he might be from the branch that "left" the family and never kept contact.