Q: When my mother tries to phone somebody from her iPhone 4, instead of her number 'Anonymus' shows up on the other phone.

Settings > Phone > Show My Caller ID > ON

You may want to contact the cellular provider. Some offer Caller ID blocking as an option. One example is Verizon: http://www.verizonwireless.com/support/features/calling_features/caller_id.html

My iPhone doesn't have the Settings > Phone > Show Caller ID mentioned above so that may be carrier specific as well.

My iPhone doesn't have the Settings > Phone > Show Caller ID mentioned above so that may be carrier specific as well.

CDMA networks (Verizon, Sprint) don't support this setting and isn't present on CDMA phones.  Virtually all GSM carriers support it.

http://support.apple.com/kb/HT4515