In my family it is commonly acknowledged that our name got changed as we were coming into America through ellis island. Despite spelling it with an "ion" we still all pronounce it with an "an". We suspect two groups of Tynans came into the country at the same time, and we were the ones that got a little screwed over.
In a way its even better, because there really are no Tynions that aren't directly related to me. I suspect I'm related to all the Tynans as well, just much more distantly.