I see many people owning a onion site uses his own server (maybe just place the server in his home?)
But traditionally for a regular non-onion site we usually buy hosting. Can I buy hosting for a onion site? Would it leak my privacy or anonymity?
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But traditionally for a regular non-onion site we usually buy hosting. Can I buy hosting for a onion site?
Absolutely! You can pay for a VPS or a managed server or even co-locate your own server.
Here are some things to keep in mind:
If you use a VPS, what will keep you provider from viewing what's in your storage?
If you use a managed server or you co-locate your own server, will the provider have access to the machine without your permission?
If your provider is sniffing packets, they can see that you are connected to the Tor network but they cannot see who visits you or what you are doing unless they break into your VM or server. I genuinely believe that most don't care what you do as long as you don't break the terms of your agreement (like setting up an exit node) or it is determined that you are doing something highly illegal.
Would it leak my privacy or anonymity?
I personally run a wordpress blog onion site on my hosted mail server. I keep it patched. I don't use any extra plugins, and I don't give it out publicly. Does my provider know that I run it? I seriously doubt it. Would they care? Probably not unless the laws change in the country where it is hosted saying that onion services are illegal.
Finally, your question is, "is there guarantee of privacy to buy onion hosting?". No. There is never any guarantee at all. They best you can do is understand how Tor and web security works and work from there. Sorry I can't give an easy positive answer because there isn't one.