This is just getting silly now. Why would he be saying his ex's name? He's drunk yes, but he's not delirious. It's understandable if he during his time with DG reflected back on his bad memories, as has been shown previously, but to think DG is his ex is a bit far fetched. Jiwon's ex "makes him feel sick', he is likely the reason why Jiwon is so guarded with his image and emotions, now he has a bit of dutch courage he let down his guard, and showed he wanted the security/contact with DG.
(Bloody hell, this comment section is getting as bad as KS where people are saying the two characters MuST BE brOTHers, just because Sangwoo's mum and Yoon Bum have dark hair!)
Well this prediction is for this story, not my own stpry, why bother.. I just state this deduction that's seems predictable, not something that what's going ro happen.. A deduction used as something that what might happen not for what exactly happen.. If this is my own story I have my own way of how it's gonna work not that what I stated before.. I have another way that at least 1 out 100 people can predict what gonna happen on my story.. Ohoho..

After Alex begging DG for not to go, maybe the next chapter will appear that Alex saying his ex's name and that make our DG went depressed and started to avoiding and ignoring Alex.. Then later he became friendly with that 'furious-senpai' and makes Alex jealous and thinking hard about his feelings and finally realized he's too, in love with DG.. And try to gain DG attentions back.. And it turned out that 'furious-senpai' also loves DG and became rivals with Alex..