public JsonResult Get()
   {
        List<Owner> owners = new List<Owner>();

        using (DatabaseContext dbContext = new DatabaseContext())
        {
            Owner owner1 = new Owner { Name = "Vik", PetsCount = 5 };
            Owner owner2 = new Owner { Name = "Viki", PetsCount = 7 };

            dbContext.Owners.AddRange(new List<Owner> { owner1, owner2 });
            dbContext.SaveChanges();

            Pet pet1 = new Pet { Name = "Snow", Owner = owner1 };
            Pet pet2 = new Pet { Name = "Chrismas", Owner = owner1 };
            Pet pet3 = new Pet { Name = "Mary", Owner = owner2 };

            dbContext.Pets.AddRange(new List<Pet> { pet1, pet2, pet3 });
            dbContext.SaveChanges();

            owners = dbContext.Owners.Include(p => p.Pets).ToList();
        }

        var json = new JsonResult(owners);

        return json;
    }

public class Pet
{
    public int Id { get; set; }
    public string Name { get; set; }

    public int OwnerId { get; set; }
    public virtual Owner Owner { get; set; }
}

public class Owner
{
    public int Id { get; set; }
    public string Name { get; set; }
    public int PetsCount { get; set; }
    public List<Pet> Pets { get; set; }
    public Owner()
    {
        Pets = new List<Pet>();
    }
}

public class OwnerAndPets
{
    public int Id { get; set; }
    public string OwnerName { get; set; }
    public int PetsCount { get; set; }
    public List<string> PetsNames { get; set; }
}

...
List<OwnerAndPets> oap = dbContext.Owners.Include(p => p.Pets).Select(x => new OwnerAndPets
{
    Id = x.Id,
    OwnerName = x.Name,
    PetsNames = x.Pets.Select(y => y.Name).ToList(),
    PetsCount = x.PetsCount
}).ToList();
...