Procedural Generation

You don't need anything too sophisticated for this. The key is Random.onUnitSphere, which gives you a random position on the surface of a unit sphere. You can then multiply that by the desired radius to move the point out further. This script gives an example. Create a Sphere game object with a scale of 0.1, assign that to StarObject in the editor. Once you have it working change StarCount to 5000 and you'll have a decent looking set of stars.

Now, using spheres for this is obviously a really bad idea, but I wanted to give a simple example of the procedural part of this. It's just repeatable randomness, and for this particular thing you don't need Perlin.

To make this efficient you could use billboards for the stars rather than the spheres. Better yet, use Pro so you can take advantage of batching - should be able to do the whole thing in a single draw call.

Another option for efficiency (again, requires pro) is to generate the random sky dome using this method, then create skybox textures using render textures, and use those for rendering a sky box. You'd have procedurally generated skyboxes that way - the best of both worlds.

 public class StarDome : MonoBehaviour
 {
   public GameObject StarObject;
 
   public int Seed = 42;
   public int StarCount = 500;
   public float MinRadius = 100;
   public float MaxRadius = 120;
 
   void Awake()
   {
     // make sure we generate the same positions each time
     Random.seed = Seed;
 
     for (int i = 0; i < StarCount; i++)
     {
       // get random position on unit sphere
       Vector3 p = Random.onUnitSphere;
 
       // move it out to the sky sphere distance, with some randomness
       p *= Random.Range(MinRadius, MaxRadius);
 
 
       // instantiate game object
       GameObject star = Instantiate(StarObject, p, Quaternion.identity) as GameObject;
       star.transform.parent = this.transform;
     }
   }
 }