What does the setting "anyone one the web" for "who can post" exactly mean?

[He_Fu]

Hi
I am setting up a group which which should be used as a DL for an external customer.
To allow email send to this DL, I need a setting of  "anyone one the web" for "who can post".
Can please someone tell me if this setting will expose the name of the group somewhere? That it can be found by someone who is not supposed to know about it?
Or can the name only be used when the name is known.?