If (as a test) you temporarily set the Outbound CID for your extension to e.g. "John Doe" <003247xxxxxxx>
and call a different mobile, does the caller ID show correctly on the destination phone?
If not, then you need to find out what your provider requires to send a number that’s not yours. It may be technical e.g. Diversion header, contractual (sign supplementary agreement) or they may not support it at all.
If the test with 003247xxxxxxx works ok, you need a hook to rewrite the 047xxxxxxx to 003247xxxxxxx before it’s sent to the trunk. See