How to mock a method call that takes a dynamic object

Moq provided It.IsAny<T> for that case

sessionMock.Setup(x => x.Get<User>(It.IsAny<object>()).Returns(new User());

*dynamic is any object

First of all, anonymous objects are not really dynamic.

If you used dynamic objects like

dynamic user1Filter = new ExpandoObject();
user1Filter.Name = "test 1";
var user1 = session.Get<User>(user1Filter);

you could mock it like

sessionMock.Setup(x => x.Get<User>(DynamicFilter.HasName("test 1")));

by implementing custom argument matcher:

static class DynamicFilter
{
    [Matcher] public static object HasName(string name) { return null; }
    public static bool HasName(dynamic filter, string name)
    {
        string passedName = filter.Name; //dynamic expression
        return name.Equals(passedName);
    }
}

You can use the It.Is<object> matcher together with reflection. You cannot use dynamic in expression trees so It.Is<dynamic> won't work that's why you need reflection to get the your property value by name:

sessionMock
    .Setup(x => x.Get<User>(
        It.Is<object>(d => d.GetPropertyValue<string>("Name") == "test 1")))
    .Returns(new User{Id = 1});
sessionMock
    .Setup(x => x.Get<User>(
        It.Is<object>(d => d.GetPropertyValue<string>("Name") == "test 2")))
    .Returns(new User { Id = 2 });

Where GetPropertyValue is a little helper:

public static class ReflectionExtensions
{
    public static T GetPropertyValue<T>(this object obj, string propertyName)
    {
        return (T) obj.GetType().GetProperty(propertyName).GetValue(obj, null);
    }
}