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)

Check out

• D.P
• Moving
• Vigilante
• The King of Pigs
• Girl K
• Strangers From Hell
• Heartless City
• Tong Memories
• Weak hero class 1
• Ordinary Day
• A Shop for Killers

If you enjoyed the action and fighting sequences of "Bloodhounds," you may consider watching "D.P.", "Weak Hero Class 1", or "Bad and Crazy". These dramas also feature strong action elements, compelling stories, and memorable characters.