No, this is not about Meredith. It's probably a family name, there's never any sign it was supposed to be a girl's name, and John was perfectly in character to tease him about it. And, no, he'll never do it in anyway but teasing - and certainly not in close moments.
This is about Madison.
"Madison" entered the current usage via a mermaid, who named herself after an avenue in Manhattan, which in turn was named after the fourth president of the United States. Who served from 1809 to 1817.
Those of you who are mathematically astute will note that the year 1812 falls in his first term of office. 1812, as in "The War of". As in the one any Canadian will say they beat us.
Insteresting name for a little Canadian girl, no?