I get that Luke and Rey used it for extended periods of time, I just think it’s strange to call it their’s when Anakin also used it and built it. If all three used it, why wouldn’t the named ownership go to the one who built it and first used it? This makes even more sense given that Luke and Rey both built their own sabers.
Especially when the color of the blade comes from the crystal harmonising with the person building the saber.