Responses
The son's name is Lee Ji Yoon (based on the phone conversation)
And since the other guy is looking for Lee Jiyoon, the son is responding in first person. It is either he and his mom has same name or his mom is using his son's name when dating.
Yes you're pretty much right, his mom was using her son's name because she wasn't serious about dating and didn't want to use her real name
well that's something for sure
translator, i know you did your best but the whole conversation where you randomly chose the first person, they're talking about jiyoon, and jiyoon is not him but his mom. that's why the dialogue makes no sense in the 1st person.