First one I read (and it's a bit older manhwa I think first one to use that trope) was Pian Pian but you have to read it somewhere else because the author was very mad when they found out mangago, so in the end mangago removed all of her works. You can read it either on Paw manga or Bata. To or some other manga site. Basically everyone has their initials of their soulmate tattooed on somewhere on their body. But the MC has the tattoo on his dick so he feels insecure. He is also a beginner chef at a high end restourant and seems to always embarrasss himself and make mistakes around the main chef that seems to always be glaring at him. It's really good story.
I didn't read much of nameverse, so I only remember one right now, there's others but I can remember. So I recomend Pian Pian, I didn't finish yet, but it's a good one.
Nameverse: is basically a universe where people are born or at certain age a name apears on the body, this name is your soulmate and when you get physical in contact with a person and the names on their body shines it's your soulmate. So usually on this universe it's see as something romantic and most people are looking for they soulmates. The name can appears on any part of the body, ah if I'm not mistake the name of the soulmates appear on similar body parts of each other.
Pian pian is about a guy who wants to find his soulmates and he wants his first time with this person, but he have a problem the name of his person is on his dick so he can't knows when he meets his soulmate, he is frustrated but still trying, until he meet his boss and things get out of hand
I'm on chapter 3 but we have a crossover? It's my first time see a guideverse and a nameverse at the sema time hehehe nice ヾ(☆▽☆)