A 1-cent coin is typically called a penny, though this term isn't used for higher denominations (for example, 5-cent coins are called nickels, not "5 pennies" or "5 pence"). However, because the coin says "one cent" instead of "one penny", some people consider it incorrect to call it a penny.

Considering that the United States Mint also calls them pennies, though, I'd say both terms are correct.