This is excellent!
What I think would be very useful to have added to this PR is to display the possible \<name><tab> (and there may be more than one) methods for inputting the character.
It might also be very useful to add whether or not the character is a valid start indentifier character or identifier character for Julia, and whether it is possible to use as an unary or binary infix operator.
Another place I think it would be great if this information were to be displayed is in the help system (in a separate PR, I guess, after #19847).
For example, if you type ?xor or ?⊻ (in v0.6), the help shows that you can enter it either with \xor or \veebar, but that was added manually just for that function. If you type ?in, it shows 4 different Unicode character operators (∈, ∋, ∉, ∌), but no information on how to enter them. Even if the help system finds no bindings for a particular Unicode character, it could display the information from #19847, plus any <name> forms, as well as the rest of the information I suggested above, about how it can be used in Julia for identifiers and/or operators.
EDIT: After discussion in the Gitter chat with @TotalVerb, I agree with him now that the extra information is Julia specific, and so should be displayed just in the help system, not in show.