First of all I want to apologize for any mistakes and potential misinterpretations. My English is poor, I'm obviously not a writer, so don't take it seriously. Just a bunch of thoughts that I finally got the courage to share. Feel free to share yours too!
Henry Letham
Some of you're probably aware that Letham is an anagram of the word 'Hamlet' which is referred to numerous times throughout the film.
I can assume that his last name also has something to do with the Latin word lētum (sometimes written lēthum) that translates to 'death', 'ruin,' destruction' in English.
Sam Foster
to foster — to look after or to take care of (a child or a young person). Throughout the movie, Sam fussed over Henry like a mother hen with one chick, so there is no denying that he was some kind of father-figure to Henry in his dreamworld. In the script, Smitty even mistook Sam for Henry's father once.
Lila Culpepper
This one might be very far-fetched, but Lila's last name reminded me of the Latin word culpa, which can be translated as 'blame', 'fault' or 'guilt'.
Athena
I'm convinced that her name refers to the Greek goddess of wisdom, war and arts/crafts. Athena got a few minutes of screen time, but she struck me as very ambitious, powerful and intelligent young woman. And she's good in different forms of art, therefore I guess Athena is a perfect name for a girlboss like her.
Tristan Rêveur
The name Tristan comes from the French word triste meaning 'sad', 'sorrowful'; 'melancholy'. Rêveur can be translated from French as 'dreamy' or 'dreamer'.
Technically Tristan Rêveur is a sad dreamer, which I find quite interesting.