His identity is not an open question. We know exactly where and when William Shakespeare of Stratford was born and baptized (in those days they recorded baptism dates, not births). We know who his parents were, who his wives and kids were, the names of his 8 siblings, and the business ventures of his family...to name a few things.

We also know when he got started in the London theater scene, and how his career and skill developed (we've found early poetry of his which was not very good, for example). We even know that he became very wealthy and famous (he was famous even during his life) due to the success of his plays, and acquired quite a bit of real estate before he died.