Jaksta does what it can to pull the name from the stream it is capturing, but if it is getting the wrong one then it will be because the stream is offering up something else as it's title.
This essentially comes down to the streaming protocol of the site and also how Jaksta reacts to it. Sometimes it can get varied titling and this can be due to small changes in the site/stream at any given time of capturing. It also can be due to the browser that the video/stream is being played in, as the browser can also affect the nature of the stream.
So my first suggestion would be to attempt the capture in different browsers and see if you get the desired (or at least different) result.
Even though it is not ideal, you also have the ability to edit the file name and some details in the Jaksta library list. It is easier to do this immediately after the recording is finished so that it does get mixed up with any others, especially if they have the same title (like what you have experienced).
I have just upgraded to version 2 of music recorder on my Mac, as the pervious version ceased to be able to stream from the BBC website. Now that I have upgraded I can now stream, but I'm not receiving the program details, I just keep getting this pc_hd_abr_v2_uk_dash_master. How do I get the program details? I now currently have 16 files with the same name. The same happened when using Media Recorder too