The title pretty much sums up the problem; if a person make a reservation, is there a word which describes that person as a person who has made a reservation?
I would much prefer "reservee" over reserver.
One to, or for, whom anything is reserved;
The rules aren't standardized, of course, but "reserve" is a French word and we often use the -ee ending in English to form the past participle, as with
employ -> employee
train -> trainee
I wouldn't really recognize "reserver" as a word. If you must have a single word for this, I'd use reservee... but I still think that the more common "reservation holder" or similar would be better.
The industry standard phrase here is "confirmed guest". It's used pretty much universally in restaurants and hotels in the US.
One could create, as Catija has done, the word "reservee", and a native English speaker would know what you meant if they were given the context, but it would not be immediately clear and might get you strange looks and a few chuckles. I also agree with Catija that technically the hotel/restaurant makes the reservation, and the guest is the person for whom the reservation is made, and therefore the hotel/restaurant is the "reserver" and the guest is the "reservee", but the distinction would probably be lost on anyone who doesn't spend their time hanging around grammar forums.