You asked if the local Congo would have a record of where you live being a 'former study'... Probably not. Usually that's something that the individuals who knew you (your Study Conductor, their Group Study Conductor, any friends you had etc) know, but isn't generally recorded in the Congo's files (maybe a former Secretary may correct that point?).
A Study Report is completed each month but as far as I recall the name was on it but not the address - maybe I've remembered that wrong, it's been some years since I completed one!
Formally, if you move from one territory to another and the local elders thought there was good reason to let the new Congo know you were around (say you have a habit of picketing the KH, or writing to JW's telling them how bad the WTS is or somthing), then they may write a letter to the new congo telling them the score. That letter would be filed and you may end up being recorded as a Do Not Call (DNC).
Informally, most of the elders in a city or region know each other and they may just discuss 'the situation' surrounding an individual. That may end up with a DNC being recorded too.
Recording a DNC involves adding your address (but no other details) to a slip of paper kept with the Territory File and being read out in the Meeting for Field Service before the group worked that territory. As I recall it, the Service Overseer kept a file detailing with the reason a DNC was recorded, maybe it was a DF/DA person, an apostate, or someone who was 'hostile' and was likley to abuse the JW's if they called, and that was reviewed by the Body of Elders periodically.
In practice, DNC's seemed to get nearly as many calls as anyone else. The elders are supposed to go to the house once a year to make sure the same person is still living there and to check if their 'attitude' has changed. It was always a change to the routine to make those calls, although as I was an MS not an elder I only got to go to the 'Hostile' DNC's, not the DF/DA/Apostate DNC's!!
I might have learned more sooner if I had of gone on those calls!
Cheers, Max