Artist Identity

Can an artist have an identity? I have been thinking about this for some time. when say identity I mean is what drives the art? what inspires the style? I was talking to an another artist, he has been in the industry since the 80's. I told him that I don't feel like I have an artistic identity, I told him that I don't have art that I am know for kind of like Pollack has a style to be known for. He told me that I do have a style, it's whatever I create and people flock to and enjoy. we talked for sometime and I came to understand that, I maybe over thinking things. Am I alone? or is this something all artist do? If you are over thinking things then you should stop because it can hold you back from being great.