I think I figured out the origin of my dad's name - Francis Smith Dane (in his case, the third). There were no Francis Smith's on our family tree, so I had originally thought that it was a combination of a longstanding Dane first name Francis with one of our ancestral last names, which was Smith. This is not in keeping with family naming tradition, though. For every Marcia Winter Anderson, there was always a Marcia Winter. (this tradition carried on to Marcia Winter Anderson Dane, my great aunt). So, there must have been a Francis Smith, and sure enough, there was. Francis Smith was a congressman from Maine in the 1830's and 1840's, and a very well-respected one. He would have been a contemporary of Joseph Dane, who was also in congress, though a bit earlier. Joseph was the great grandfather of Francis Smith Dane I. I don't have any anecdotal evidence to support this, but it seems highly plausible given the naming conventions in our family.
By the same token, I discovered that Peter Thacher Smith, who is on my Dane side, was in fact named after Reverend Peter Thacher, who is an ancestor on my paternal grandmother's side. Peter Thacher was influential in the training of Reverend Thomas Smith, Peter Thacher Smith's father. As Grandma Edie (Thacher) used to say "we're all cousins."