Need help finding an ancient Greek and an Egyptian myth of somesort.

by JMusik

I remember seeing a video, telling that ancient Egyptians believed, that a person dies a second time, after his name is forgotten.

Another thing told I'm that video was a Greek mythology about some hero who had to chose a reward. Either be immortal or be remembered forever.

I tried googling but I couldn't find anything. Either these "facts" are lies or I suck at googling.

Gadarn

With regards to the Greek one, Achilles was told by his mother Thetis that he had two possible fates: a short life, but eternal glory or a long life but no glory.

Mother tells me,
the immortal goddess Thetis with her glistening feet,
that two fates bear me on to the day of death.
If I hold out here and I lay siege to Troy,
my journey home is gone, but my glory never dies.
If I voyage back to the fatherland I love,
my pride, my glory dies. . . .
true, but the life that's left me will be long,
the stroke of death will not come on me quickly.