You have a "2 clause BSD" licence. What you call the resultant license is irrelevant. What matters is the text of the license. Heck, you could call it a "modified 3-clause BSD license, please see LICENSE" if that's what you want.
Come on, is saving face that important to you? "2-clause BSD" already has a well-accepted meaning. You might as well have said that GPL refers to "Gary's Perfect License"; After all, it's a GPL.
I only commented because of the attitude that removing the second clause from the 3-clause BSD license was not an option because we already have a 2-clause BSD license.
Fair enough. This thread started with "Why not 2-clause BSD", and I understood your comment as defending the use of "2-clause BSD" in a non-standard way.