Caller ID is an odd thing because each carrier maintains their own database and they only sync whenever they feel like it. We've had times where we ask a carrier to change the caller ID on one number and a person's Comcast will see the update in a day or so while others will take months or longer.
The short answer is that it's a carrier issue. I know Verizon recently made showing the account name an option on my account, so if you don't see that in your carrier's account management page you should try calling them. But if you want your number to be blanked out and just the text shown, I doubt they'll go for that and just tell you to hit whatever * combination hides your number before dialing.