What's The Best Way to Change 3 Bools For Real Time Morning, Afternoon And Night

If it can only be Morning, Afternoon or Night (3 states) at any given moment, you should not use 3 booleans (they can represent 8 states). You can avoid bugs such as all 3 booleans becoming true just by choosing your variables in way that prevents it.

 using System;
 using UnityEngine;
 
 public enum TimeOfDay {
     Morning,
     Afternoon,
     Night,
 }
 
 public class TimeOfDayStart {
     public int StartHour;
     public TimeOfDay Name;
 
     public TimeOfDayStart(int startHour, TimeOfDay name) {
         StartHour = startHour;
         Name = name;
     }
 }
 
 public class MyScript : MonoBehaviour {
 
     public TimeOfDay currentTimeOfDay;
     public static readonly TimeOfDayStart[] TimeOfDayStartHours = {
             new TimeOfDayStart(4, TimeOfDay.Morning),
             new TimeOfDayStart(12, TimeOfDay.Afternoon),
             new TimeOfDayStart(20, TimeOfDay.Night),
         };
 
     void Update () {
         var now = DateTime.Now;
         currentTimeOfDay = TimeOfDay.Night;
         foreach (var tod in TimeOfDayStartHours) {
             if (now.Hour >= tod.StartHour) {
                 currentTimeOfDay = tod.Name;
             }
         }
         Debug.Log(currentTimeOfDay);
     }
 }