It does open a tiny dialogue box, inviting you to start typing the person's name.
It's a test: Were you thinking about the person's name, or were you only thinking about the info you're looking for in their previous emails?
So my problem with it is I often am not particularly thinking of the person's name at all. Or at least not their full name. Or how to spell it if it's more unusual than 'Jane Smith'. I'm thinking here's a new email from the rep from that company which does that job for us - let's just have a reminder of where we left things with the previous job... <click> Oh. Gone.