Are you saying you want your number to just say a city or something?

CNAM is just the text that belongs to the CID when a phone service does a dip in a LIDB. If there is other info shared, I am not aware of it. I personally like the anonymity of VoIP, but I do prefer my name to show along with CID for the numbers I call.

You can use the CID block to keep this info from being passed to non-Toll-Free numbers. Most Toll-Free seem to get the CID likely due to billing and such.