Among pro-Unionists in Alabama during the war, I found quite a few people named for Andrew Jackson and other presidents. I had to chuckle, however, at the prospect of anyone in Alabama after the war (pro-Union or not) naming a child after Abraham Lincoln (or John Brown or U.S. Grant). I believe the odds of this would be about the same as someone in South Carolina naming a child after William Tecumseh Sherman.
Why? Animosities had been so great between neighbors who'd taken different sides and people were so tired of conflict, I don't believe they wanted to do anything else to add to it. But if anyone can document these names showing up in post-war Alabama, I'd be interested to hear about it.
My best guess, though, is that Alan's tongue was firmly in cheek as he was completing that post.