It’s not flattering to you and it doesn’t really add anything to you, whether you do it online or in person. And it’s such a damn cliche. If you really are independent, then stop talking about it. Just be it and shut up about it. Whoever needs to know all about your independence, will find out in due time. If you are not independent, stop deceiving others and yourself.
More importantly – who cares and who should care about whether you are independent besides you? Whether you pay your bills or your parents do doesn’t make you any more or less sexy, smart, nice, interesting, otherwise fun to be around. Lose the term and you will be much better off.