Yes each station would require a call sign. At least in the US, all call signs are publicly discoverable and the records include the physical address of the station.
There is, by law, no form of privacy about where the station is located, nor any of the communications by amateur radio.
Per FCC part 97.23 last amended in '98 you need a US mailing address where you can get USPS mail delivered. In case they want to send a complaint mail, for example. If your postal address bounces they'll cancel your license. The FCC needs a way to contact you and USPS is the one method they demand, not email, not facebook, not phone number, postal mail.
99% of hams, if not more, use their home street address which is probably where their station is located. School clubs usually use the main school address and at a giant uni it never works. Some people use PO boxes, or work address. APO/FPO addresses work fine if you're stationed overseas.
With certain weird limitations related to the national radio quiet zone by the radio telescopes and the NSA monitoring posts, the FCC doesn't care where the transmitter is located under part 97. Consider mobile operation or portable operation. You're probably thinking of part 73 "regular ole AM/FM radio broadcasting" where the FCC wants all kinds of detailed latitude / longitude data and surveys or maybe part 11 for the emergency broadcast system.
Mine has a PO box. So do others I know. My street address is not listed by the FCC. Not that I'm trying to prevent that. Just wanted to state a few facts.
There is, by law, no form of privacy about where the station is located, nor any of the communications by amateur radio.