One way to approach that is to update the mention markup to include a data-fullname attribute that contains the fullname, then you can use CSS to make it show next to the mention.
Similar to (for putting the post number on each post next to the timestamp)
a.post-date:after {
content: "#"attr(data-post-number);
}
Not sure if the Discourse team would be opposed to adding such a data attribute to mentions, but if they aren’t, it makes this solvable for the Enterprise scenario pretty quickly.