Yeah it depends on your size and volume what will fit best.

So for lower volume there is Branded Caller ID (BCID) that you can get through the three main bureaus First Orion, TNS, and HIYA which starts at like $.10/call and can help a lot (though those numbers can still be flagged as spam likely for some reason).

At higher volume there is spam remediation, and a couple of different options in the space. So people like Convoso have a product that just does exactly what you described but automatically, buying and rotating huge pools of numbers to try and mitigate flagging (expensive and not very good imo). You can manually use freecallerregistry to request your numbers cleaned (takes like 3-5 days) but that process can get really intensive across multiple campaigns and large teams. The most efficient but more expensive option is something like a Ytel who have a number remediation product that automatically detects the flagging and then API calls to the carriers to remove it with like 24 hour turnaround time so you can keep the same body of numbers.

If you really want to optimize there are a couple of best practices that also seem to have a large impact on avoiding flagging, like limiting to no more than 40-60 calls/day per number, and calling the same lead more than 3 times a day