そもそもこの手のものはstaticメソッドにするべきだと思います。

Script.cs

using System;
using UnityEngine;

public sealed class NameIncidenceTuple : UnityEngine.Object, IEquatable<NameIncidenceTuple>, IComparable<NameIncidenceTuple>
{
  [SerializeField] public string Name;
  [SerializeField] public int Incidence;
  
  public override bool Equals(object other) => Equals(other as NameIncidenceTuple);
  public bool Equals(NameIncidenceTuple other) => !(other is null) && Incidence == other.Incidence && Name == other.Name;
  public int Compare(object other) => Compare(other as NameIncidenceTuple);
  public int Compare(NameIncidenceTuple other)
  {
    if(other is null) return -1;
    if(Incidence == other.Incidence) return Name.Compare(other.Name);
    return - other.Incidence + Incidence; // 発生確率の大きいものを先頭にする
  }
}

public sealed class SetIncidenceSample : MonoBehaviour
{
  [SerializeField] public NameIncidenceTuple[] Pairs;
  private int Sum;
  
  int CalcGCD(int a, int b) => b == 0 ? a : GCD(b, a % b);
  
  void Start()
  {
    Array.Sort(Pairs);
    var GCD = Pairs[i].Incidence;
    for(int i = 1; i < Pairs.Length; i++)
    {
      if(GCD <= 1) break;
      var incidence = Pairs[i].Incidence;
      if(incidence == GCD)
        continue;
      if(incidence < GCD)
        GCD = CalcGCD(GCD, incidence);
      else
        GCD = CalcGCD(incidence, GCD);
    }
    Sum = 0;
    for(int i = 0; i < Pairs.Length; i++)
    {
      Sum += Pairs[i].Incidence / GCD;
    }
  }
  
  public string GetMonsterNameRandom()
  {
    var random = UnityEngine.Random.Range(0, Sum);
    //しきい値を超えるインデックスを探します
    int threshold = 0;
    for (int i = 0; i < Pairs.Length; i++)
    {
        threshold += Pairs[i].Incidence;
        if (random <= threshold)
        {
            return Pairs[i].Name;
        }
    }
  }
}