On October 12, 2012, a Twitter user named woodmuffin tweeted the following:
San Marino is the only country that rhymes with a former NFL quarterback's full name— woodmuffin (@woodmuffin) October 12, 2012
Naturally, I couldn't let this claim go without verification, so I wrote a script to get every NFL quarterback from NFL.com, found a big list of countries, and then wrote a script to naively find the rhyming ones by matching the last three letters of each quarterback's name with the last three letters of the country name to produce this list.
The closest I can find are "Joe Flacco" (currently still playing) for Morocco and "Warren Moon" for Cameroon. It's surprising how well the last three letters strategy worked to find rhymes, though. Here's a last four letter matching list for comparison.
Of course to be sure that there are no exact rhymes, I would need to use a more sophisticated algorithm, but for a quick script this isn't too bad!