Politely, I guess.

[sitifan]

Welcome to Greek. My name is Dr. Mounce, otherwise known as Bill. I don't care what you call me. Politely, I guess. I've always been called Bill my whole life. I'm kind of partial to the name, but I know for some of you that's difficult. So choose which name or title you're comfortable with. No fear. A lot of what some of you are going to have to deal with is not real. It's fictional. (My bold.)
Source: https://www.biblicaltraining.org/learn/institute/nt201-biblical-greek/nt201-01-the-greek-language

What does the expression in bold mean?

 

[emsr2d2]

I think he means that he doesn't mind what you call him as long as it's something polite.

 

[Tarheel]

This one doesn't have a firm handle on the English language. If you keep reading his stuff you are going to keep having questions like these.

(There is an expression that goes: "I don't care what you call me as long as you don't call late for dinner.")

 

[Flask]

I don't care what you call me. Politely, I guess.

. . . What does the expression in bold mean?

At its grammatical face value, it seems to mean, "I guess you can call me by the name Politely."

I agree with emr2d2 about the intended meaning, which might have been better expressed with a different lead-in:

I don't really care how you address me. Politely, I guess.

In other words, "I" realize that "my" only concern regarding how "you" address "me" is that "you" do so politely.