In https://html.spec.whatwg.org/multipage/form-elements.html#the-fieldset-element

The name of the group is given by the first legend element that is a child of the fieldset element, if any. The remainder of the descendants form the group.

I wasn't able to find another use of “name” in the sense that it is defined here, that is, I couldn't find any reference to how such a name would be used.

The term seems to be causing some confusion in w3c/csswg-drafts#1584 so this is a request for some clarification, and/or perhaps calling it the “legend or label”of the group (or “caption”, to be consistent with how <label> is defined) so it's at least clearly not the same as the name of the <fieldset> element.

The name attribute represents the element's name.