pet.cs

void Main()
{
  var myPets = new List<petInfo>();
  var yourpets = new List<petInfo>();

  myPets.Add(new petInfo("me", "dog","Rex"));
  myPets.Add(new petInfo("me", "fish","Goldy"));
  myPets.Add(new petInfo("me", "iguana","Spikey"));

  yourpets.Add(new petInfo("you", "dog","Spot"));
  yourpets.Add(new petInfo("you", "cat","Tigger"));
  yourpets.Add(new petInfo("you", "bird","Polly"));


  var result = myPets.Union(yourpets).Select(x => 
  {
    if (x.Owner == "me") 
      return new { PetType = x.PetType, MyOwnerName = x.Owner, MyPetName = x.PetName, YourOwnerName = "",    YourPetName = ""};
    else 
      return new { PetType = x.PetType, MyOwnerName = "",      MyPetName = "",        YourOwnerName = x.Owner, YourPetName = x.PetName};
  });
  
  result.Dump();
}

public class petInfo
{
public string Owner;
public string PetType;
public string PetName;

public petInfo(string owner, string petType, string petName)
{
    Owner = owner;
    PetType = petType;
    PetName = petName;
    }
}

This was written for LINQPad4 -- so that is why I have the Dump() call. Remove that line if you are not using LINQPad4