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.
Japanese Language
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Remember that you can add furigana to your posts by writing ~{KANJI|FURIGANA}~ like:
~{漢字|かんじ}~ which comes out as:
{漢字|かんじ}
If you are talking to someone asking about Ken, it's the first. If you are talking to Ken, it's the second.
If you are Ken, you have amnesia.
(Yes, it is possible to refer to oneself by name, but it would be quite awkward / weird if one do it in real life.)
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