public static Pet pet;

// somewhere

pet = new Pet()
{
    Name = "Bob",
    Age = 12
};

// later

Console.WriteLine("Welcome " + StartMenu.pet.Name);

public static Pet pet;

// somewhere

pet = new Pet()
{
    Name = "Bob",
    Age = 12
};

// later

Console.WriteLine("Welcome " + StartMenu.pet.Name);