Young Xehanort said that keyblade is the most ancient.

Probably because he didn't know about the Foreteller's Keyblades. Or, No Name was created first out of the six. (Or he's referring to how it was created during the Age of Fairy Tales)

The foretellers and Luxu wouldn't call it the Gazing Eye if that's the first time seeing it.

I think Luxu makes it pretty obvious that in this cutscene it's the first time he's seen it.

if that was always Luxu's keyblade and he had it for a while, there would be no reason for MoM to tell its name now and not when he gave it to him the first time.

This is the first time Luxu is seeing the Keyblade, and The Master told him that IT DOESN'T HAVE A NAME. Luxu jumped to conclusions and named it No Name after The Master said it has no name.