Pilot reported a NMAC with another aircraft that had a similar call sign while trying to set up on final at an airport with a temporary tower.

Narrative

I was flying into ZZZ for the [event]. A temporary Tower and ground facility was setup to accommodate the increase in traffic. I received ATIS approximately 15 miles south east of the airport and made an initial radio call to Tower that my intention was to enter a right downwind for Runway XX (which was the runway in use). Temporary Tower told me to call when we had entered the downwind. There were many other aircraft in the area and one particularly with a similar call sign Aircraft Y (I was Aircraft X) who was approaching from the north. I called my right downwind and was given a landing clearance. Around the same time I had heard Aircraft Y also receive a landing clearance. I specially asked temporary Tower if Aircraft X could fly a normal pattern for landing as I had not seen Aircraft Y. Temp Tower told me that it was approved. I flew a normal base to final and as I leveled my wings there was another aircraft at my altitude also appearing to be in landing configuration. The other aircraft must have seen me first as they were making evasive maneuvers. I called traffic in sight and verified Aircraft X was clear to land. And landed without further incident.