If you want to feel like one of the community "bobbies" of London, patrolling the cobblestone streets of a market square and knowing every shop owner you see, this is about as close as you'll get.
There's always some measure of fame when you work with the public in a position of authority. Every single store manager, shift supervisor, and nosey janitor will know you by first name. Your presence will be felt and recognized by gangs of loitering youth. If you slide tackle a perp when he heads for the door with a lavender-scented candle tucked under his hoodie, you might even end up on the local news.
You might also end up on the wrong side of a lawsuit. Please don't slide tackle anyone on mall property. That's probably not the right kind of famous.