It's a pretty normal thing in Japanese, yes. You'd know from context which meaning it is based on who you're talking to.

If you are talking to someone asking about Ken, it's the first. If you are talking to Ken, it's the second.

I'm not a fluent speaker, but I'm pretty sure it depends on who is being talked to. Like if you're talking to someone else, it would mean the first one, and if you're talking to Ken, it would mean the second one.

In text though, it would give you context for you to guess who is talking to who. For example, someone could ask the question, and in the next line, Ken answers. Or maybe only this person and Ken are in the room.

Edit: autocorrect

I'm not a native speaker and quite out of practice but I would lean towards the first translation being more correct. The second doesn't seem wrong but would be spoken with different pacing for me to interpret it like that and not be confused. I've actually had someone ask about me that way (iirc, 8+ years ago), but it was a group discussion and it was used to ask a question that had already been asked of another person, and then continue to ask questions without further specifying me as the subject by name. Native speakers leave out the subject way too much and its confusing as fuck and it may have been said that way intentionally for those of us who were not.