This is something I was always confused about even before Bethesda bought the Fallout IP.
Let's be honest, the Pip-Boy 2000 has that mascot red hair boy on it, but anywhere else it shows the Vault Boy instead (and this is in the old games). Literally the only time it shows the red hair one in on the Pip-Boy surface, then if you go into the actual Pip-Boy screens (Perks, Karma, Skills, SPECIAL, etc) it is only depicted Vault Boy
.
Back in the day that really messed up my OCD, but then I tried to reach a logical reason for it to be like that (so I wouldn't get frustrated by my OCD
) and thought that Vault Boy is the Vault Tec mascot and that red haired character is the Pip-Boy's mascot (probably even called Pip-Boy himself). This is of course all made up by me, the lore doesn't provide any base for my reasoning. But oh boy, it did calmed my OCD a lot!