Games like Silent Stay
Games like Silent Stay include MiSide, Outlast, Sally Face - Episode One, Mouthwashing, and No, I'm not a Human. We matched them by the tags players give Silent Stay on Steam (Interactive Fiction, 3D, First-Person, Adventure, and Horror): closest matches first, and among equally close ones the better-known games.

MiSide
Shared: Psychological Horror · First-Person · Horror

Outlast
Shared: First-Person · Horror · Psychological Horror

Sally Face - Episode One
Shared: Psychological Horror · Horror · Story Rich

Mouthwashing
Shared: Horror · Psychological Horror · Story Rich

No, I'm not a Human
Shared: Horror · Psychological Horror · Indie

Layers of Fear (2016)
Shared: Horror · First-Person · Psychological Horror

SOMA
Shared: Horror · Psychological Horror · Story Rich

Little Nightmares
Shared: Horror · Adventure · Atmospheric

Buckshot Roulette
Shared: First-Person · Horror · 3D

Amnesia: A Machine For Pigs
Shared: Horror · First-Person · Interactive Fiction

Poppy Playtime
Shared: Horror · First-Person · Psychological Horror

Little Nightmares II
Shared: Adventure · Horror · Psychological Horror

Firewatch
Shared: Adventure · First-Person · Story Rich

Dagon: by H. P. Lovecraft
Shared: Horror · First-Person · Interactive Fiction

Blair Witch
Shared: Adventure · Horror · First-Person

Fran Bow
Shared: Psychological Horror · Horror · Adventure

What Remains of Edith Finch
Shared: First-Person · Story Rich · Adventure

Visage
Shared: Horror · Psychological Horror · First-Person

Outlast 2
Shared: Horror · First-Person · Psychological Horror

Garten of Banban
Shared: First-Person · Horror · Psychological Horror

Escape the Backrooms
Shared: Horror · Psychological Horror · First-Person

Welcome to Kowloon
Shared: Horror · Adventure · First-Person

Amanda the Adventurer
Shared: First-Person · Horror · Adventure

Still Wakes the Deep
Shared: Horror · First-Person · Psychological Horror