Games like The Hat Man
Games like The Hat Man include Poppy Playtime, No, I'm not a Human, Phasmophobia, Sally Face - Episode One, and Outlast. We matched them by the tags players give The Hat Man on Steam (Horror, Psychological Horror, Atmospheric, First-Person, and Realistic): closest matches first, and among equally close ones the better-known games.

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

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

Phasmophobia
Shared: Horror · Psychological Horror · First-Person

Sally Face - Episode One
Shared: Psychological Horror · Horror · Dark

Outlast
Shared: Horror · First-Person · Atmospheric

SOMA
Shared: Horror · Psychological Horror · Atmospheric

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

Mouthwashing
Shared: Horror · Psychological Horror · Atmospheric

Layers of Fear (2016)
Shared: Horror · Psychological Horror · Atmospheric

MiSide
Shared: Psychological Horror · Horror · First-Person

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

Visage
Shared: Horror · Psychological Horror · First-Person

Amnesia: A Machine For Pigs
Shared: Horror · Atmospheric · Psychological Horror

Firewatch
Shared: Atmospheric · First-Person · Adventure

Subliminal
Shared: Psychological Horror · Realistic · Atmospheric

DON'T SCREAM
Shared: Horror · Psychological Horror · Atmospheric

What Remains of Edith Finch
Shared: Atmospheric · First-Person · Mystery

Backrooms: Escape Together
Shared: Horror · Psychological Horror · Atmospheric

Little Nightmares II
Shared: Horror · Atmospheric · Psychological Horror

Little Nightmares
Shared: Horror · Atmospheric · Dark

Welcome to Kowloon
Shared: Horror · Psychological Horror · Atmospheric

Pacify
Shared: Horror · Psychological Horror · First-Person

Fears to Fathom - Ironbark Lookout
Shared: Horror · Psychological Horror · Atmospheric

Amnesia: The Dark Descent
Shared: Horror · Psychological Horror · Atmospheric