Can some suggested me some Korean movies or dramas to watch?

Since you mentioned "My Name" and "Bloodhounds" I believe you like thriller dramas and movies. So I'll recommend you some really good thrillers.

Movies

• Parasite 
• The Call
• The Witch: Part 1. The Subversion
• Train To Busan

Dramas

• All of Us Are Dead 
• Big Mouth
• Flower of Evil 
• Happiness
• Mouse 
• Revenge of Others
• Squid Game
• Tale of the Nine-Tailed 
• The Glory
• The Glory Part 2 
• The Smile Has Left Your Eyes
• Vincenzo
• W

Series:

Crash Landing on You (2019)

Memorist (2020)

Extracurricular (2020)

Revenge of Others (2022)

How to Buy a Friend (2020)

Taxi Driver (2021)

Bitch X Rich (2023)

Movies:
Target (2023)

The Man from Nowhere (2010)

Ballerina (2023)

Queen of Tears: A legal drama involving the pride of a village and the heiress of a conglomerate.
Wedding Impossible: Follows the life of an extra actress with unacknowledged talent.
The Midnight Studio: A unique story about a photographer who takes portraits of ghosts.