first - what you described (mafia/crime/ action /anti hero ML +romance) is MY FAVORITE scenario, so maybe you could also recommend what you've seen like that, beginning with "my name" which I couldn't find, can you link it?
I just commented in other tread and will copy it because fits what you want perfectly:
there are good dramas, but really really BEST ever drama in Crime/action/romance is "Cruel City", it's so high level no other will compare to it... you would love everything in it, twists and turns, unexpacted surprises, character developments, action and interesting events TILL the end (many dramas have good start but then goes down, but it was perfect 20 episodes), you never know what will happen next, who is whose ally or enemy, mafia, undercover cops and gray characters, I mean no one is fully good and only few fully bad, this drama is complex and not usual cliche black/white sotry. Many multilayered characters and complex relationships but ML is best, someone like K2 + more smart and more dark, anti hero/criminal authority.
+ one of most amazing romance (though it's kind of side story not main, but still one of best and emotional romance I've seen, with hot chemistry), btw from my experience best not cliche romances are often as side story in not romantic dramas.
p.s. after "Cruel City" I'm always hungry for something like this drama, I hoped few times (for example when I tried Vincenzo, also "My beautiful bride") but every time after few episodes I realize that this isn't even close...
other anti hero-bad guy ML dramas with romance (starting with better ones as drama overall):
Arthdal Chronicles it's totally different genre, like korean GOT but really best drama ever and amazing multilayered characters, there are 3 main male leads and 2 female leads. almost no one are fully good in this drama, complex interesting characters and relationships, there are no guns but killing and being bad guy ... of course. one ML is good (but also interesting development) other ML is bad cruel super smart misterious and super sexy though he isn't in first episodes, he is surprise and twist himself, and third ML older guy amazing soooo interesting character, he is national hero and also anti hero, really amazing character with also amazing romance, his love interest is soo badass girl...and their romance is great, 2 ambitious strong leader person on opposite sides of political battles still loyal to each other. there are other romances too...
Flower of Evil really high level drama, amazing acting. dark ML, romance (they are married but trust me still better romance then 70% kdramas)
Hello Monster ML isn't bad but not angel either, but there are 2 other SMLs serial killers, there is romance too (I'm not fan of that romance but this is must watch drama, really!)
The Smile Has Left Your Eyes misterious dark ML and amazing chemistry romance Sora Kara Furu Ichioku no Hoshi this is original Japanese version, both are very good
Kill It perfect fit for you - contract killer and detective girl, both beautiful, chemistry and really good drama
Lucifer also perfect fit for you, masterplan revenge and dark SML behind it, he kills people with other peoples hands, smart dark almost villain and nice beautiful girl....
Born Again hard to explain but ML practically is killer obsessed with FL, there is love triangle and 2 different time/reincarnation
A Man's Story and Giant in both bad guy/anti hero and FL romance, overall not so great dramas but very good romances. first one is more bad, villain second is anti hero who tries not to be fully bad ))) Giant is long drama, I skipped other storylines and watched only Joo Sang Wooks story/romance, and it was worth it, one of memorable romances (I think)
The Innocent Man revenge drama, how good boy becomes bad... he did everything for woman but she betrayed.
Warrior Baek Dong Soo historical and not so much romance (I mean romance is there but it's weak part) but I recommend it because SML is unforgettable anti hero, he fully shadows ML Ji Chung Wook he becomes kind of mafia boss and he plays cold killer with sad beautiful eyes soo great!