string[] value1 = {"A","B"};
string[] value2 = {"C","D"};

List<string> value1 = new List<string>() {"A","B"};
List<string> value2 = new List<string>() {"C","D"};

var output = {"AC","BD"};

var output = {"AC","BD"};

var output = value1
  .Zip(value2, (v1, v2) => v1 + v2)
  .ToArray();

var output = Enumerable
  .Range(0, Math.Max(value1.Length, value2.Length))
  .Select(i => (i < value1.Length ? value1[i] : "") +
               (i < value2.Length ? value2[i] : ""))
  .ToArray();