Games like My Name Is
Games like My Name Is include Firewatch, What Remains of Edith Finch, Outlast, Poppy Playtime, and Layers of Fear (2016). We matched them by the tags players give My Name Is on Steam (Horror, First-Person, Adventure, Mystery, and Atmospheric): closest matches first, and among equally close ones the better-known games.

Firewatch
Shared: Adventure · Atmospheric · First-Person

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

Outlast
Shared: Horror · First-Person · Atmospheric

Poppy Playtime
Shared: Horror · First-Person · Mystery

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

METRO 2033 Redux
Shared: Horror · Atmospheric · First-Person

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

METRO Last Light Redux
Shared: Horror · Atmospheric · First-Person

Fears to Fathom - Woodbury Getaway
Shared: Horror · Adventure · First-Person

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

Metro 2033
Shared: Horror · Atmospheric · FPS

Metro Exodus
Shared: Horror · FPS · Atmospheric

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

BioShock™ Remastered
Shared: Horror · Atmospheric · First-Person

Resident Evil Village
Shared: Horror · First-Person · Action

Atomic Heart
Shared: Adventure · Horror · FPS

Bendy and the Ink Machine
Shared: Horror · First-Person · Mystery

Black Mesa
Shared: First-Person · FPS · Action

Resident Evil Requiem
Shared: Horror · First-Person · FPS

BioShock™
Shared: Atmospheric · Horror · FPS

Five Nights at Freddy's: Secret of the Mimic
Shared: Horror · First-Person · Adventure

The Room
Shared: Mystery · Atmospheric · Adventure

Among the Sleep - Enhanced Edition
Shared: Horror · Adventure · First-Person

The Hat Man: Shadow Ward
Shared: Horror · First-Person · Adventure