The name for both edge and vertex creases is simply "crease" as specifying
the domain in the name would be redundant.

This is problematic actually, since a geometry component is in an invalid state if the same name is used on two domains.

I'm also not sure about whether this should be added as a builtin attribute. Lately we were discussing whether crease should actually be a builtin attribute.
We thought it might make more sense as a "reserved name" attribute, meaning operators would expect to use a point domain float attribute with a specific name, but it wouldn't be otherwise guaranteed.
The general idea is limiting the number of built-in attributes, making the workflow more generic. Regrettably, the main reason we added crease as a builtin attribute is because "the spreadsheet looks too empty on the edge domain".

Somewhat related, the subdivision surface node should probably get a "Vertex Crease" input.

I tend to agree with Hans here. Although I wouldn't call it "reserved name" (which usually implies that the name can't be used for something else) but "naming convention".

Regrettably, the main reason we added crease as a builtin attribute is because "the spreadsheet looks too empty on the edge domain".

I don't remember that to be the reason tbh. We just wanted to be able to access that information with geometry nodes.