This is a question that only you can answer, but how badly do you need to know who made the call?
If you have been receiving nuisance phone calls then you can just report them to your local police station and they will take it from there. If you trust them to pursue it then that should be the matter resolved. If you really want to be certain the appropriate action is taken then you need to get in touch with their service provider. The police may not have the power to do anything, but their service provider will be interested that one of their customers is behaving like that and it could lead to the individual making the calls being cut off or worse.
The problem is you can’t phone their service provider without using a reverse cell phone website as without those websites there is no way of knowing who they are with (unless you phone their voicemail and they haven’t changed their message then sometimes you can tell from that). So even though there is a small charge then the best option is to just use it and discover the service provider and the details of their name and address.
The police will be able to do a lot more if they already have the name and address as you have provided it, then just to make sure go to the phone company too.
That combo gives you the best chance of getting the person into trouble (just make sure it wasn’t a wrong number first!). That doesn’t necessarily mean the person will stop, they can get a new phone to call you from etc - but having their name gives you an advantage and if you let them know you are aware it is them then most people will be too cowardly to carry on when you obviously know it is them.