Pennsylvania means "Penn's woods." Quaker William Penn was granted the tract of land by King Charles II of England in 1681 as repayment of debt owed to Penn's father, Admiral William Penn. Originally, Penn suggested Sylvania (woodland) for his land.

Painting of Treaty of William Penn with Indians by Benjamin West -
public domain image on Wikipedia

"Commonwealth" of Pennsylvania

Pennsylvania shares the designation "Commonwealth" with Virginia, Kentucky and Massachusetts. The word is of English derivation and refers to the common "weal" (well-being) of the public. In 1776, the state's first constitution referred to Pennsylvania as both "State" and "Commonwealth" (either term can be used correctly today). In Pennsylvania, all legal processes are carried out in the name of the Commonwealth.

Source:

PA Symbols: Pennsylvania Historical & Museum Comm.

Links:

State Name Origins - 50 States