Coming to the Buddha Dharma does not make you a Buddhist. An infant or adult ceremony does not make you a Buddhist. Coming to the Cleveland Buddhist Temple does not make you a Buddhist. There is another ceremony for that, but not this one.
Then why do it? For many different reasons. As adults we do it because we did not find teachings elsewhere to help us navigate this life with more peace and calm. We do it to reinforce our desire to hear the teachings, put them to the test and if they work, to continue on this path with the support of our Sangha.