When an E-4 calls me "hey" or "hey man" knowing that I am an officer, should I bother to correct him?

This cannot be a real question- immediate adjustment, Sir!

Humm does he realize he is talking to the same person? You did say you don't work together, does he recognize you are an officer? When I was at WR off post you didn't know who. Sounds like it's gone on so long you feel some kind of way about calling it to his attention. Since you have failed to correct it he might feel your ok with it. Since it has gone on for it seems like a while without you saying anything (why don't you call it to his attention), but to blast him at this point are you blasting him because he is wrong or because you didn't correct when you should have? Sir. I agree that when you ignore a failure to meet the standard, You have set a new standard that seems to be the case Sir.

This might be ancillary to the question, but here is a story from the Title 32 side. I am a member of the California State Guard (the Militia, as mentioned in the 2nd Amendment of the US Constitution, for the State of California). My first assignment was as Deputy Commander to a Brigade-level unit. I was a Lt Col (CA), and the Commander was a Col (CA). We were chatting in his office, one day, and he invited me to address him by first name. While I readily agreed, I also insisted that (at times) it has to be name/rank (traditional). He allowed me to explain: When it's just him and me, first names are okay. However, if there was anybody else present, I will be using name/rank. The reason is that if I, the Deputy Commander (the second highest ranking person in the unit) shows respect for the Commander, then there is Absolutely No reason for anybody else to not do so.

He sagaciously nodded and accepted my rational.

I've known many officers that outside of the work place always said call me by my first name especially if we were at a club outside the post.... I dated a female officer from my unit and we kept it quiet.....

Ignore it!! While working and he addresses you with sir is all that matters....

Ignore it!!

I’m more confused as to why a Captain should need to ask for such advice. Is this an example of todays leadership? This is a no brainer or did you not learn this in OCS or West Point?

Absolutely

NO ONE in the military should be saying HEY MAN.

We teach what we allow.