What does Gideon mean?
From the Hebrew verb gada, 'to hew down, cut off,' hence 'hewer' or 'feller' — fitting the judge who cut down Baal's altar (Judges 6). The common 'mighty warrior' gloss is a secondary association from his role, not the meaning of the root; because no noun is formed from the verb, the exact nuance stays somewhat uncertain.
What does Simon mean?
From the Hebrew Shimʿon, “he has heard.” Simon Peter is chief among the apostles.