I doubt it's possible

Imagine the spam you'd receive if people could anonymously text you things

Oh that ability exists, ie Burnerapp, where you can just use a number then burn it.

But Im talking completely no name or number. Appls like Burner use a random number, then when you need to change it, you burn it and use another.

I'm trying to think of a legal use case for this and to be honest I can't really come up with a good one. This is not possible for a very good reason.

Can you prefix the SMS number with ##31## (or similar) - typically you can do this on a phone call to suppress caller-id

1. Gain access to her phone.
2. Change the contact name to "unknown" or something like that.
3. Hope she doesn't check the number stored for the contact.

Edit: not overly familiar with Android, this would work on iOS.

 SIMs are only a couple of bucks or so to buy? Just get a fresh new one and use it.