Jews in concentration camps had to be marked in some way for record-keeping and identification purposes.
On Weisel's first night in Auschwitz, he is assigned to Block 17, where he is to sleep in a bed with another boy or man. On the afternoon of his second day there, he is lined up with other prisoners and they are given tattoos on their left arms, three people at a time. His is A-7713. This operation was run by the Nazis, but the tattoos were administered by Weisel's fellow Jews.
This number becomes his name, as far as the Nazis are concerned.
This means he arrived in Aushwitz in 1944, as this is when the A series of arm tattoos were in use. Contrary to popular belief, Auschwitz was the only concentration camp that tattooed its prisoners.