Actually an edge case
(1) As others have said, your ticket is not valid on EC379 from Hauptbahnhof until Südkreuz. Nobody will care: this is a journey of five minutes, and it is quite unlikely that you will meet a conductor who is on duty but not busy with something else (like answering desperate questions, telling people where not to store their bags etc). You may or may not want to risk the adventure of these five minutes.
(2) For regional transport within Berlin the exact wording of the point of departure as written on your ticket does matter. (But prepare for railway/S-Bahn/BVG staff who do not know or understand the precise meaning of these ever-changing details issued by DB Fernverkehr who is not their employer.)
Key point is whether or not you have a City-Ticket included. A ticket from "Berlin Südkreuz + City" (or "BERLIN + City" in the good old days, see @Inconspicuousseagull's answer) should be valid for a single journey on RE/RB/S/U/tram from anywhere within Berlin AB to Südkreuz station; a ticket mentioning e.g. "Von [i.e. from] Berlin Schönhauser Allee" would allow only a direct[definition needed] trip from that precise station. I am not sure which one they sell as a Super-Sparpreis these days…
Yet I do not believe that your ticket is "from Berlin Prenzlauer Berg" – simply because there is no station (or stop) with that name (and the borough named Prenzlauer Berg has lost its official status & local parliament in 2001, only a certain fame remains). So we have to know what else you got. (You did not buy a ticket from Prenzlau[provincial town 100km north] by accident, did you?)
Note that your ticket may contain an extra timetable information (mentioning there that "this is not a ticket"). If "Berlin Prenzlauer Allee" appears only in that timetable section (and not in the actual ticket), then you are fine.
(3) Let's assume you do actually have a ticket from "Berlin Prenzlauer Allee" (or any other station in the Prenzlauer Berg neighborhood). If so, you are entitled only to a direct trip from that point of departure; yet in Berlin's dense railway network you often have more than one route option.
In times of normal schedule one of your reasonable choices would be to take the S-Bahn to Gesundbrunnen, and then some regional train (RE3, RE5, …) to Südkreuz, passing through Hauptbahnhof. (Not a detour, and nominally as fast as Ringbahn, albeit less frequent/reliable.) Hence taking a regional train from Hbf to Südkreuz should certainly be covered by your ticket.
Unfortunately the regional service from Gesundbrunnen to Hauptbahnhof is temporarily suspended for construction works until 2024-12-13 (while Hbf to Südkreuz is still running). So if you do your trip in these two weeks to come, you can take the southbound RE3 / RE4 starting in Hauptbahnhof, but might then get into trouble explaining how the heck you have made it there (if anybody takes the time to verify your itinerary on-the-fly, and dares to ask).
Again very unlikely as this is a journey of seven or eight minutes (so little time to argue), and regional trains through Berlin tend to be crowded (I might be more concerned of getting off at the proper destination).