Yes, I moved a shop many years ago about 2 miles down the same busy street. They were renovating my old location-in a shopping plaza. The way it was set up, no one could tell I was even there. Had to change the first 3 numbers on my phone. Put a big sign in the window of my old shop. Even tho we moved closer to the competition, we gained clients because of better visibility. I even needed to hire another full time groomer! If you ever watch the movie Bingo, you can catch a glimpse of my old (moved) shop (think I had sold it just before they shot the movie). As long as your clients know where you are, and the phone company gives out the new number, you'll be just fine.
Old groomers never die, they just go at a slower clip.