∅proper
One thing I want to remind you of, even if it is perhaps a bit late in the day: Proper names are now DPs. Anything that can get a θ-role is a DP. But the name part itself is actually just an NP—see the handout and/or p. 260 in the Adger textbook.
The practical upshot of this is that pretty much any time you have occasion to draw a proper name, it will now have a structure like these:
DP DP DP
/ \ / \ / \
D NP D NP D NP
∅proper Pat ∅proper New Jersey ∅proper Qdoba