Princess has a point. You apologize and tell them your real name, along with a background.

You were born on a farm in a quiet town and had a simple youth. Your siblings made certain you remained in school and studied a vast number of subjects. You tried a number of things growing up, but found your special talent in metallurgy, explaining your cutie mark. Your family was supportive but sad by your decision to move off the apple farm and begin your training as a blacksmith. You still visit your brother and sister, but your grandmother has since passed on.

Your name is Applebloom. Your cutie mark is a hammer hovering over a red anvil with a leaf hanging off of the step, making up the anvil’s horn.

You finish up by telling them they don’t have to give you their names. They can consider this information part of the apology.

The only information they offer so far is that they were also born in Ponyville.

The three of you are warmed up enough to try something else.