It isn't possible with the current design of your code. The reason is, you can not reference 1 field of the object in another field before the object is fully constructed. That is same as why we can't use 1 field value in another while declaring as class level varibales.
However, there are ways you can achieve, what you want to.
Option 1:
const string titleText = "Grooming";
List<Reservations> reservations = new List<Reservations>()
{
    new Reservations{title=titleText, className=checkColor(titleText)},
};
private static string checkColor(string title)
{
 ...
}
Option 2:
    class Consumer
    {
        List<Reservations> reservations = new List<Reservations>()
        {
            new Reservations{title="Grooming"}
        };
    }
    class Reservations
    {
        string _title;
        public string title
        {
            get
            {
                return _title;
            }
            set
            {
                _title = value;
                className = checkColor(title);
            }
        }
        public string className;
        private string checkColor(string title)
        {
            return "";
        }
    }