The character who sells badges in Paper Mario 64 is Merlow. He runs a badge exchange in Shooting Star Summit, where Mario trades collected Star Pieces for special badges.
Merlow’s selection includes useful badges such as Peekaboo, which displays enemy HP, Zap Tap, which damages enemies that physically touch Mario, and Feeling Fine, which protects Mario from status conditions. Other offerings improve HP or FP recovery, increase coin rewards, or alter battle effects. Prices range from a single Star Piece to much larger amounts.
Merlow is part of the fortune-teller family connected with Merluvlee’s home. Merluvlee provides paid clues about collectibles and upgrades, while Merlow focuses on badge exchanges. Their location is easy to overlook because it is not the same as Rowf’s Badge Shop in central Toad Town.
That distinction explains the common mix-up in this question. Rowf sells a rotating selection of badges for coins, while Merlow trades a fixed collection of more specialized badges for Star Pieces. Tayce T. is a cook, Kolorado is an archaeologist, and Rowf is the owner of the separate town badge shop.