The sailor, George Mendonca, and Rita, had just exited a movie theatre upon hearing the news of the war's end.
There were several other kisses - between guys (service members) and gals - and there were 2 photographers present, U.S. Navy photographer, Victor Jorgensen, and contract photographer, Alfred Eisenstaedt. Each man took photographs of the scene.
Alfred Eisenstaedt later recalled seeing a sailor kissing several women, but Eisenstaedt had turned away from that observation/perspective for a bit ... and when he turned back, he saw George Mendonca grab and kiss the nurse (see note/link below).
The fact that Rita [later to be Mrs. Mendonca] is in the picture, tends to challenge the other sailor candidates.
Mendonca has sometimes been spelled Mendonsa.
CBS New story about the couple; 2012