Privacy to disconnect your identity from the service? There is no solution to this. Full stop. Even with Tor, the state backed acronym entities will figure it out if you get on their radar.
If your objective is to keep your service online, you’re going to be hard pressed to find cost effective alternatives… Commercial solutions are expensive, like, “if you have to ask about the price, you can’t afford it” expensive.
Alternatively, you can try to roll your own by having many many proxy servers yourself… but if you’ve got a target on your back, you’ll never have enough instances; DDOS-as-a-Service is much cheaper than the amount of reverse proxies required to keep your service online.
There’s probably other use cases, but chances are, you’d still be hard pressed to find a solution that’s cost effective.