How to round to nearest even integer?

Try this (let’s use Math.Round with MidpointRounding.AwayFromZero in order to obtain “next even value” but scaled – 2 factor):

double source = 1123.0;

// 1124.0
double result = Math.Round(source / 2, MidpointRounding.AwayFromZero) * 2;

Demo:

double[] tests = new double[] {
     1.0,
  1123.1,
  1123.0,
  1122.9,
  1122.1,
  1122.0,
  1121.5,
  1121.0,
};

string report = string.Join(Environment.NewLine, tests
  .Select(item => $"{item,6:F1} -> {Math.Round(item / 2, MidpointRounding.AwayFromZero) * 2}"));

Console.Write(report);

Outcome:

   1.0 -> 2     // In case of tie, next even value
1123.1 -> 1124
1123.0 -> 1124  // In case of tie, next even value
1122.9 -> 1122
1122.1 -> 1122
1122.0 -> 1122
1121.5 -> 1122
1121.0 -> 1122  // In case of tie, next even value