You can change your caller ID settings, but in that case, they will see neither your name nor your number.
If I recall correctly, my carrier used to have an option where you could change the name that appeared for caller ID. This was mostly intended for people on family plans who wanted to have their own name rather than the account holder's. It's been years since I even looked for something like that. However, if your carrier offers such a feature, you could change your name to your number. Of course, if people have your information stored in Contacts, it will show up on the screen as however they have you saved. That could be "John D. Doe" or it could be "Squidgee Widgee."