Thanks for your question.
The iPhone is comprised of two different messaging protocols: IMessage and Text message. Both of which are affiliated with your phone number. There is an option, however, of setting your iMessage to display only your Apple ID. If your Apple ID does not include your name, you could get away with imessaging somebody and them not knowing who it is.
In order to appear as though you're texting from a different number, you can use an alternative messaging app from a selection in the app store. This will conceal your actual phone number.
Try downloading the TextMe app from the app store. This is one such app that allows you to message from an alternative number.
Once you have done this, hit 'compose' and you can go ahead and message any recipient with your alternate number!
I hope this helps.