Weyl and Weil knew each other's work well. Weil will have known Weyl at the Institute for Advanced Study, and I suppose they talked about Weil's ideas on fibre bundles, while Weil was teaching in SE Pennsylvania. Weyl died before Weil joined the IAS.
Their specific family histories were too far apart to suggest any identifiable common ancestor. But did either of them ever comment that the family names are etymologically the same?
I am not asking about the spelling, pronunciation, or history of these names. I do wonder whether either of these men publicly took notice of (i.e. commented on) the connection.
For example I too have heard that Weil commented on possible one-day confusion of his name with Wiles. He was enough of a linguist to know "Wiles" is not etymologically kin to "Weil" -- and certainly to know in contrast "Weil" and "Weyl" are minor variants of one name. Did he ever talk about that?