Baker is the bread surname. From Old English and Middle English words for a person who bakes, it named the specialist who baked for a household—or, just as often, the person who ran a village’s communal oven and took a cut of loaves as fee.
That second detail matters: baking was everyday labor, so the surname is widespread and polygenic. Baxter is a related occupational form (historically often feminine). Dutch Bakker and German Becker sometimes translated to Baker in the US. The family-friendly meaning stays concrete: flour, oven, and crust—not a metaphor for “someone who cooks up ideas.”