All that tells us is that there was a man from Stratford called Shakespeare and that, for whatever reason, his name appeared on a number of plays attributed to him. That does not prove that he wrote them. 
We don’t even know if that is how he spelt his name. The only surviving example of Shakespeare’s writing are six scratchy signatures spelt several different ways.
There is also significant evidence to suggest he did not write the plays. What we know of his education suggests he would not have had the necessary schooling to produce works of the calibre attributed to his name.