public static string GetMemberName<TResult>(Expression<Func<T, TResult>> expression, ExpressionType expressionType)
{
    switch (expressionType)
    {
        case ExpressionType.Call:
            var methodCallExpression = expression.Body as MethodCallExpression;
            if (methodCallExpression == null)
            {
                throw new InvalidOperationException("Expression must be of method access.");
            }
            return methodCallExpression.Method.Name;

        // Another expression types...

        default:
            throw new InvalidOperationException("No appropriate expression was passed.");
    }
}

this.GetMemberName(obj => obj.MyMethod, ExpressionType.Call);