iMessage, the Apple “BBM” sometimes encounters a few small problems. Indeed, it happens that the number associated to iMessage, even when the SIM card is changed, remains in memory. For example, you have a new iPhone but your SIM card (more exactly its number) is still linked to the previous iPhone : the new owner may receive your iMessage.
First of all, turn off iMessage ( Settings -> Messages -> iMessage ).
Then, disable FaceTime, often linked to the same account. ( Settings -> FaceTime -> FaceTime )
Turn off the iPhone, then put the correct SIM card in your smartphone.
Turn the iPhone on and activate both services. If everything goes right, a message “Waiting for activation” should appear. You can then check in Reception if the number, and eventually the e-mail address, are correct.
The easiest way to avoid problems is to avoid changing the SIM card when your phone is turned off, which tends to reboot settings on this precise point.