Her name is pretty quirky—she came up with it by combining the first letters of three Pokémon: Teddiursa (Te), Mareep (ma), and Cubone (cu).
Temacu's romantic life is basically a running gag. She first fell for Brock after he caught her when she nearly tumbled into a fountain while chasing her Nidorina. She immediately decided they had to get married and started daydreaming about their wedding, though Brock was awkward and clearly uncomfortable about the whole thing.
That crush evaporated pretty fast. When Team Rocket accidentally captured her instead of a Pokémon from her father's lab, James ended up catching her as she fell from their balloon. That was apparently all it took—now she wanted to marry him instead. Team Rocket saw an opportunity and pressured James to go along with it so they could raid the lab. He hated it. Temacu even made up a story about James saving her from "terrorists" when she introduced him to her dad.
By this point Brock had actually started developing real feelings for her, so watching her fawn over James crushed him. When Misty exposed Team Rocket's disguises and they made their escape, Temacu jumped in front of a Water Gun attack aimed at James to protect him. She got hit and passed out.
Her father later revealed she'd become obsessed with marriage after watching her cousin's wedding. When Temacu woke up, she'd moved on to her next crush—her doctor, who actually reciprocated her feelings this time.
Content compiled by AnimeList.moe from publicly available sources.