People in Shakespeare's day had no concept of a "real name". Thus William Shakespeare's name is William Shakespeare even though the entry in the baptismal register reads "Guliemus filius Johannes Shakspere", or in English, "William the son of John Shakspere" The number of spelling variants for Shakespeare's last name is legendary, and as far as Shakespeare's contemporaries were concerned, none was more "real" than any other. Centuries of custom have hallowed the form "William Shakespeare". This is the standard spelling. You can call him "Guliemus Shakspere" if you like, but this is no more "real" than any other spelling.