No, you’re not going to ask him to cure your rad poisoning instead, inquire about facial reconstruction. Head on over there and look to the right of the center noodle shop.
Luckily, just as there is a barber available, there is also a plastic surgeon in Diamond City. But what about after you spend time out in the Wasteland with your character? What if you want their appearance to change in accordance with what they’ve experienced? Or maybe you just plain ol’ are sick of seeing the face you originally made.
Fallout 4 is a huge fan of character customization.