Ira:
I don't see "me" anywhere. But the problem is not my iOS, it's my Mac. When I send a test text (or any other text) from my iOS or from my Mac, it just shows my phone number, not my name on the Mac side. In other words, when I sent a test text to myself from my iOS to my Mac, it says from Rita on my iPhone but when it gets to my Mac, it just has my phone number. When I send a test text from my Mac to my iPhone, the mac just shows my phone number but the iOS which receives the text shows my name.
It's probably not a big deal, but when I send a text to someone, I want to make sure it has my name, not my number, so they won't have to look it up to see who it belongs to.
I just tested it on my iPhone, but unlike you, I am running the latest version of iOS. My name does show in the To window.
Also check your listing in Contacts. When you look at the alphabetical list, it should show the word "me" at the end of the line where your name is. Not in the full contact info page, but on the alphabetical list of all your contacts. If it doesn't, check to see if someone else is identified as "me". If so, you can change it back to you.
