I personally feel like the "well known" persona comes more from the Next Mutation, personally. Or at least the third movie. The "pizza addicted surfer speech" being applied to all of them wasn't really a thing until the original turtlemania was on its deathbed in the mid-90's as far as I can tell. However, because people remember that better, it's what stuck.
My personal thoughts of their general attitude was looking at a bizarre situation, saying "Welp...time to deal with this" and just going with it. At least very early on. Seasons 1-3.
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