Sending caller ID across country lines can be problematic. There's no way to ensure that what you send actually shows up correctly on the other end - some countries and carriers use caller ID formats that are incompatible with others, while some carriers are simply broken and can't accept caller ID at all.
When sending a foreign caller ID (for example a U.S. caller ID to a phone in the U.K.), the local carrier or even the user's handset may try and localize the number, displaying it as if it were a local call. In the U.S. to U.K. example, a caller ID of +14075550100 might be displayed as 0407 555 0100 on a UK phone.
Regulatory issues can also affect your caller ID. Who is allowed to see and set caller ID can vary by country; privacy rules can be ambiguous and up to carrier interpretation, leading to inconsistent caller ID support among carriers even in the same country.