I only have a single (residents only) tavern, designated from my only communal dining room. There is no overlap penalty, you only get that if you paint two locations over one another.
As far as I can tell, the tavern also functions as a dining room. I see dwarves with the 'dined in a legendary dining room' thought, so it must work somehow.
However I sometimes see dwarves grabbing a meal from one of my meal stockpiles that is outside the tavern, and eating it on the spot.
So I'm not 100% sure if the dining room works exactly as intended, or that it only works because I also have a prepared meal stockpile in there (so when a dwarf grabs and eats a meal from that stockpile, it eats in the dining room location)
EDIT: it seems to be the latter. It looks like if you designate a tavern from a dining hall, even if it is your only dining hall, dwarves will no longer use it as a dining hall.
Followed some dwarves closely. If they take food from my prepared food stockpile that is not in the tavern, they will either eat it there at the spot, or claim the (single) table in the library for eating it (which gives no legendary dining room thought, and gives a dined at a crowded table thought if the second chair on the opposite end of the table is in use.
If they take food from the prepared food stockpile inside the tavern / dining room, they will eat it at the spot if there's no seat availble in the library, without sitting down at a table. They will get the legendary dining room thought though, so putting your prepared meals stockpile inside the tavern/dining room is a workaround, as long as you keep the tables and chairs in other locations to a bare minimum.