Both are fan translations tho...
The "let me have the title of euihyun’s lover… please" seems to be MTL. Just put it in Google Translate. It pops almost the identical thing. The second one ("let me be your boyfriend, date me.") sounds more "natural" to me and sounds more like Taeju to me than the first one...
The original sentence is 김의현 애인 타이틀 달라고. 나랑 좀 만나줘...
The phase "김의현 애인 타이틀 달라고." in Korean translates to "I want the title of Kim Ei-hyun's lover." It sounds too robotic in my opinion.
The phrase "나랑 좀 만나줘" in Korean translates to "Please meet with me" or "Please go out with me" in English. It's a request for someone's company or time. The word "나랑" means "with me," and "만나줘" is a polite request form of "meet." So, it's like asking someone to spend some time together.
So to me, while the first uploader probs used a translator and left it at that, the other one seems to try to make it more natural sounding. Both are still plausible but you can just wait for the official.
Maybe try reading the first panel where it says that it's a fan translation or just look at the title of the chapter and the fact that it's missing the typical " official translation".
sometimes i prefer the fan tl bc its a lot closer alto the original and retains the essence and syntax. official tls try Too hard to change dialogue. “let me have the title of euihyun’s lover… please” vs “let me be your boyfriend, date me.” like be so serious rn