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when I call some cell phones the caller ID shows my city and state rather than my name
The provider of whomever you're calling is responsible to show the Caller ID. For example, if you call Frank (a Verizon subscriber), Verizon provides the Caller ID for Frank...not Cox.
If Frank calls you, then Cox provides the Caller ID.
If Verizon is only showing your City State, Verizon is not looking up your phone number to your name. Each lookup costs money...0.004 cents..so Verizon is either saving cash or Caller ID rules are different for cellular companies.
Nothing you can do to resolve.
You might try "Caller ID Per Call Blocking" (*67) to see if it will just block everything.
"Caller ID Per Call Blocking prevents your name and number from being displaying. on a per call basis". (That's a copy and paste from Cox's website. My high school English teacher would haunt me if I wrote something like that).