That's very strange. I was thinking that you didn't save well your contact phone number on your phone, but if when you send the message it shows his name, then all I can think of is a bug with your biteSMS app you are usingTaUs the stock SMS app doing the same? If it's the SMS stock app doesn't do that then it's definitely biteSMS. but if yes the stock app does the same, then go to setting> contacts> mails, contacts, calendars> 1.) sort order = last, first
2.) display order = first, last
Then reboot your phone and try receive a message from your contact.
Also one detail that I forget to ask in my previous post is to know if this happens with anyone you receive message from? Or just only one contact?