I thought about this after looking at my oldest Pokemon from a previous thread. Some of my Pokemon have unique stories and thought people might enjoy sharing their stories. Here are mine.
Larry-Larry was my first Dragonite. She was named before genders were a thing in Pogo. Unfortunately, she had SW/HB. When TMs came about, I turned her into a DT/H Dragonite, and powered her up. Never changed her name.
NightRunner-Rapidash. When I first started playing PoGo, I was on a military TDY. I hatched this girl on a military base, from a pokestop on a military base. Pokemon don't spawn on military bases, so I ran at night to hatch eggs. This low kick/fire blast Rapidash was my first Snorlax counter.
Muk-level 40 caught it at the Mall of America. Walked 220 km with it during an event to get the candy to power him up...before they were raid bosses.
Hitmonchen-I have an 88cp Chen that I caught at Cox Pavilion in Las Vegas going to an MMA fight. I also got a Primeape in LV.
Heracross, Hitmonlee, and Corsola-2 regionals and 2 fighters I was able to grab while helping the hurricane relief effort in Puerto Rico. I have fighting Pokemon from all over!
WildBush-my first wild caught Tangela, my favorite grass Pokemon. Also caught her in PR, with great IVs.