Since they were using a real person's name as inspiration, lawyers from NBC apparently reached out to Peyton Brewster, who was then married and going by Peyton Rutledge, to get permission to use her name (via Mental Floss). Clearly she was okay with it! Rutledge even had an appearance on the show. In season two, episode nine, "The Search," she plays a teacher named, as you might guess, Mrs. Rutledge (via IMDb). Rutledge has a line in the show where she says, "Punky Brewster? Strange name!" (via Mental Floss).
Tartikoff passed away in 1997 (via Haaretz), and George Gaynes, who played Punky's adopted father, Henry Warnimont, passed away in 2016. But Soleil Moon Frye, who plays Punky, says with the reboot, "I really feel like [Gaynes] and Brandon Tartikoff are looking down, so excited and proud" (via Cheat Sheet).
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