You can hear the track name by using the read title bar command, NVDA t.
I wonder if other screen-readers read the tracks when they change. This would need to be a setting that could be turned on and off.
Perhaps this should be a general setting, automatically read the title bar when it changes in the opened Window. Then you could set up a profile if you only want it to be done in a specific program.
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I think the best you can get is by Alt-Tabbing from WinAmp to a different Window and back, at which point you hear the track title.
One thing I have noticed, and I don't know if it's a Windows update that has made this happen, but all of a sudden I can navigate the playlist window and NVDA will read the tracks and I can hit enter to start that track playing. Until maybe two weeks ago all I could do was play a directory and enqueue more files if I wanted and then manually skip forwards with the CTRL+b shortcut.
It has always been a bugbear that I can't navigate the playlist on my Dell laptop because I can on my Microsoft Surface Pro tablet, and both versions of WinAmp are the same and both are using the latest stable release of NVDA.
Sometimes if I have a couple of hours-worth of tracks lined up in Windows that I want to play again, I'll go to the playlist and, although I can't navigate it or hear what the title of the first track is, I hit enter and the playlist starts playing. Then, about two weeks ago, I heard the track title and, lo and behold, I can navigate the whole playlist window again. Needless to say I'm totally delighted by this, though haven't installed any new software lately so, other than perhaps a Windows update, I can't think how it happened! :)