Interesting point. Maybe "Adder" was the last name of someone in the family tree, or a mispronunciation of "Addie" or "Adair" that got passed down.
Whatever the source, at least it's easy to spell and pronounce.
I had a tough time figuring which of SIX Captain Samuel Robinsons I descended from in VT and MA.
They were all cousins, alive at the same time.
The problem is these days, it's almost impossible to figure out who the fathers are.
You NEVER really know for sure, even in the old days, but at least there was a better chance before society fell apart.