I wan to hide/show my caller id from my activity programmatically. I tried to find it in the android documentation but without the luck. Maybe you have any ideas?
The Caller ID is network specific not something that the phone controls. In fact in certain mobile network configurations the phone doesn't even 'know' its own phone number.
Some networks support sending an activate/deactivate caller ID network command. In GSM this is normally #31#. It can be permanent or on a per call basis.
Some networks support both, some only support one of them, and some do not enable it. Try your luck and try prefixing the dialed number with #31# and see if it works.
http://www.gsm-security.net/faq/gsm-caller-id-clip-clir.shtml