I think internally the RMS called it the F3 until the alpha numeric routes were rolled out, I'm not sure why the public knew it as the F3 (Im not a local to the area) and I don't believe it was ever signed as F3 either.
It was also in the Sydway maps with an F3 route marker from at least edition 2 1996 (I don't have edition 1), until edition 17 2014 when the alphas were then marked in the book.
I also remember when the Hume Mwy was being widened from Narellan Rd or so north bound there was a nation building project sign with 'F5 widening' as the project name.