You can set your Share Name ID to show your name, or just a generic "Wireless Caller" with the number. However, if you are one of their contacts, you will likely show up as whatever they have you listed as in their address book.
This also only works with other Verizon phone users. Not everyone will see your personalized name on their caller ID screen. You'll still be "Wireless Caller" to any non-Verizon user.