Lou Gehrig's parents were German immigrants named Heinrich Gehrig and Christina Fack.
His father is Andrew Holtz and i think his mother is Shirley Holtz
Julius Caesar's parents names were Gaius Julius Caesar (same as his) and Aurelia Cotta.
You would say "What are your parents' names?" Names is plural, so the word are would be the correct choice. Is should be used when the subject is singular.