Your students see you for who you are whether you embrace it or attempt hide it.
Students are almost always good at reading their teachers. The time you spend in front of them, by itself, gives them ample opportunity to read you; add to that the social-status acuity of teenagers and you can be fully confident that your students will know a lot about you, and quickly.
Given that, I think the right strategy is to embrace your sense of self as an asset in your teaching. Don’t overshare about your personal life, but do teach as yourself.
The connection you build when you embrace your self will improve the daily experience of your students – and you – and more importantly their learning outcomes.