One of the longest female characters in the soap EastEnders is Pat Butcher (or Pat Evans), known for her super-sized earrings, not to mention the most husbands - most notably Frank Butcher!
In Iliad or other Trojan War fanfics, the nickname "Pat" is often used for Patroclus, the Greek hero Achilles' brother-in-arms NOT lover. But let's not go into that.
A famous bearer is Pat Buchanan, who served as the senior advisor to American presidents a while back, these presidents were Richard Nixon, Gerald Ford, and Ronald Reagan.