The difference is that one (varname) is an attribute of the box, and the other (name) is an attribute of the object. In Max 4, there was no difference (for the user) between the box and the object, and boxes had no attributes, so this was envisioned as a way to assign a pattr object's box a name, without having to do it via the Max 4 'Name...' dialog.
In Max 5, the difference between object and box is slightly more pronounced, and boxes have their own attributes. Such as 'Scripting Name'.
I'm a little loathe to remove one of the two attributes, since there may be applications which depend on the one or the other. Undocumenting the object's name attribute, while leaving it active, is a possibility, but has other downsides (like lack of documentation of an important feature of the object). So, until I have a better solution, sorry for the duplication in the Inspector.