AutoMapperIssue.cs

    public class ObjectUnderTest
    {
        private readonly MappingEngine mappingEngine;

        public ObjectUnderTest(string prefix)
        {
            var configuration = new Configuration(new TypeMapFactory(), MapperRegistry.AllMappers());
            configuration.CreateMap<Person, PersonModel>()
                .ForMember(x => x.Name, y => y.MapFrom(orig => prefix + orig.Name));

            mappingEngine = new MappingEngine(configuration);
        }

        public PersonModel MapObject(Person input)
        {
            return mappingEngine.Map<Person, PersonModel>(input);
        }
    }

    public class Person
    {
        public string Name { get; set; }
    }

    public class PersonModel
    {
        public string IDoNotExistInPerson { get; set; }
        public string Name { get; set; }
    }

    [TestFixture]
    public class TestClass
    {
        [Test]
        public void Test1()
        {
            var test = new ObjectUnderTest(null);
            var result = test.MapObject(new Person {Name = "world"});

            result.Name.ShouldEqual("world");
        }

        [Test]
        public void Test2()
        {
            var test = new ObjectUnderTest("Hello ");
            var result = test.MapObject(new Person {Name = "world"});

            result.Name.ShouldEqual("Hello world");
        }
    }

Here's another way to potentially do what I think you're trying to do. You'll have to internalize your use of AutoMapper inside your ObjectUnderTest if you're going to use it that way, the static method will not help.