we might think it's to cover up the fact that he killed him
Except WE already know different. And future audiences aren't going to be that dumb that they're not going to go "hey...wait a minute. Young jedi named Darth Vader? That he TRAINED? he never trained anyone but Anakin. Who, coincidentally, lost a lot of his limbs and swore loyalty to the Emperor in the last movie...nah, Obi Wan is just trying to cover up for killing Anakin, that's all it is."
That's not plausible. Ben gives away the secret in Episode IV to anyone who's seen the first three. You have to be VERY WILLFULLY ignoring what's going on by that point to fall for that sort of editorial misdirection. Or not paying any attention at all.