As @Sergey K. said in his answer there are several ways to do this. One of these is using dxdiag tool (obviously it will only work on Windows) particularly dxdiag /t variant that will redirect the output to a given file. Then you can process that file to get required info:
public static void main(String[] args) {        
    try {
        String filePath = "./foo.txt";
        // Use "dxdiag /t" variant to redirect output to a given file
        ProcessBuilder pb = new ProcessBuilder("cmd.exe","/c","dxdiag","/t",filePath);
        System.out.println("-- Executing dxdiag command --");
        Process p = pb.start();
        p.waitFor();
        BufferedReader br = new BufferedReader(new FileReader(filePath));
        String line;
        System.out.println(String.format("-- Printing %1$1s info --",filePath));
        while((line = br.readLine()) != null){
            if(line.trim().startsWith("Card name:") || line.trim().startsWith("Current Mode:")){
                System.out.println(line.trim());
            }
        }
    } catch (IOException | InterruptedException ex) {
        ex.printStackTrace();
    }
}
Generated file will look like this:

And output will look like this:
-- Executing dxdiag command --
  -- Printing ./foo.txt info --
  Card name: Intel(R) HD Graphics Family
  Current Mode: 1366 x 768 (32 bit) (60Hz)