Can I call the News section something else on my site?

Yes. In Memberships (under Income in the sidebar), each website has a What This Section Is Called field. Type the name you want (Newsletter, Dispatch, anything) and save. It changes the heading on the posts page, the crumb trail above each post, and any menu item pointing at that page, all at once, including menu items that still carry the section's old name, "Off Mic".

It only changes what readers see on that one site. Your posts stay one library across the account, and each site can use its own name.