1. I've never seen this actor before, but his name rings a bell. Is he famous?
2. I don't think I've heard this song, but the title does ring a bell.
3. That name doesn't ring a bell, at all. I don't think you've mentioned it to me.
4. Our manager said he's mentioned that product to us several times, but it just doesn't ring a bell for any of us.
5. Does that name ring a bell? It sounds like I've heard it before.
When a name rings a bell, it means you vaguely or slightly remember it, but you can't fully recall.