When I send a iMessage to another phone it displayed my name not my number.
How ever when I receive a iMessage from two different iPhones I try and save the number to a name but it still just shows the number when I revive a iMessage not the saved name.
But one other friend of mine I saved the number and it displays it revertime with a iMessage.
The other two phones are in my house is it makes a difference. I'm on orange and one is vodaphone