Hi Antoine,
Yes you can use any DNS domain for email, as long as it is provided by a registrar involved in propagation, and you have access to records (AKA zone).
Note: this is known to work with 1st-level domains (xxx.com, xxx.net, etc), I never tried with subdomains (xxx.anyprovider.com).
Of course next question to come is: where, how?
The selfhosted Murena Cloud setup is quite straightforward, as long as you carefully read the doc and fulfill the prerequisites.
Once installed and after optional tuning, it’s effortless to run (call it “Fire and Forget” 
).
About hosting by a provider and privacy:
- for enhanced privacy, you may rent a physical server instead of a VPS, but it’s way more expensive. As these hardware are often too powerful for a simple selfhosted, you may share with friends or other activities, for the sake of profitability
- whatever is the underlying hardware, network interception is very unlikely as everything is encrypted unless you choose otherwise
You may also add a additional layer for network security: Securing your self-hosted using CrowdSec (this apply to other hosting solutions, too).
The mandatory tips for choosing your hosting are:
- you must have access to PTR reverse record (IP address to DNS name): it is mandatory to have email to work correctly (checked by selfhosted setup script, won’t go further if not properly setup). AFAIK, some pure-Cloud providers won’t allow PTR editing unless you build an expensive complex set-up (Azure, AWS, etc)
- avoid residential IP address for your server (like home ISP): some whole networks are flagged in anti-malware worldwide databases or suffer filtering by ISP, and email may not work at all
- it is very important nowadays to maintain a very good “reputation” if you want your email traffic to work flawlessly; having a “clean” IP address for your email server is very important to have in mind (*). Pure-Cloud players and residential addresses ranges often fails into “bad actors” category (although pure-Cloud providers often have leverage to “clean up” an address or range, but it’s time-consuming with their support)
(*) I had once a provider delivered a public IP address that was previously used for spamming/fishing: despite all my efforts I had to resign and ask the provider for a new one!
Please note that in some places, renting a VPS is cheaper than the electricity bill for a home-hosted … 
Last reminder: with a selfhosted, no matter where is it, your data will always be your data. That means: you can always copy/move your data out of the server, and cancel. So it may worth a try!
Hope this will help you, please ask if you need further details or any help.