In situations like this I just give them an old phone number of mine that was disconnected years ago, so in reality you are still giving them "your" number. This also gets around having to remember your fake number or make one up.

Just last week I was at the auto parts store and they asked me my phone number. As a knee-jerk reaction, I gave them my disconnected phone number from five years ago. Guess what? They still had MY actual info under that number even though I hadn't shopped there in over a year!

The system works! (sort-of) LOL.