Is Shakespeare a pen name or is it his real name?I know he is real but I'm unsure about the name.

Shakespeare is Shakespeare's real name.  He was born in Stratford-upon-Avon in 1564, and his father's name was John Shakespeare.  He married Anne Hathaway in 1582, and a daughter was born six months later.  They also had twins, Judith and Hamnet, who died young, in 1585.  Judith lived until 1662. 

Virtually nothing is known about Shakespeare's life from 1585-1592.  By 1592, however, he is at at least fairly well-known on the London stage.  And the rest, as they say, is history.

But, again, yes, Shakespeare is his real name. 

 (Source:  The Cambridge Guide to Literature in English)