Sometimes these things are possible, but mostly they aren't.
Some families stayed in one place for centuries. Others moved around, and the records didn't keep track of where they came from.
Not all Claytons descend from the Clayton-le-Moors family. There were over a dozen places called Clayton, and there were other unrelated Clayton families named after other Claytons. A Clayton family in south Yorkshire presumably originated from Clayton near South Kirkby, once called Clayton-in-the-Clay.
A Y-DNA project could identify your family, but first you'd have to connect your Clayton to some living Claytons who've been tested.
As for Robert de Clayton b 1030, it's a bit unlikely that there ever was such a person. WikiTree tends to think a source is a source and we believe anything anybody tells us. But an unsourced source is poor evidence, and the Clayton family book account is completely unsourced. It would be useful to find out what's behind it, if anything.