Yes, it’s possible. I use postfix virtual domains to direct entire subdomains to my personal mailbox, which I then host with dovecot-imap. For spam reasons I cannot in practice recommend redirecting an entire domain like <anything>@blahblahblah.com but subdomains like <anything>@addresses.blahblahblah.com or something like that works fine (and can be very secure, since if you’re using it for account signups it makes it very difficult to predict what email you’ve used for a given account making it difficult for someone attempting to reset your password or attempt to find re-used passwords across different accounts for example).

I will agree with everyone else that starting a new mail server, especially in this day and age, is a challenging and complicated task with many obscure and tedious steps and constant maintenance and vigilance and little room for error. I have been doing this for over 20 years, and even I have been blacklisted countless times for small mistakes and configuration errors, and while an increasing number of blacklists are automatic and will eventually remove you once the problem is fixed, getting off certain blacklists is difficult and in the case of some of them, effectively impossible without paying money or coordinating with your ISP (and often paying money to them instead to vouch for you, or to give you permission to even run an un-blocked email server in the first place).

Running a mail server requires a massive investment in trust and reputation, that presents a significant and possibly insurmountable barrier to entry for a novice, and it is absolutely jumping into the very deepest possible end of shark infested waters. I won’t say it’s impossible, but you’re going to have a very difficult time if you expect to be able to use it even for full-time personal use.

I will say that receiving is usually easier than sending, so if you just want to receive emails on your own server and store them there, and then send using an “official” address (not on your server) that might work better. But it’s still super complicated, and having a setup like that can make it even more complicated, so this is still really not something I’d recommend if you’re new at self hosting and networking and stuff.

There are lots of cool things you can do so easily with self-hosting, this is absolutely one of the hardest, and while it is rewarding and valuable in its own way, I would say it’s far from the most rewarding or valuable thing, and considering the difficulty, it’s almost certainly not the first thing you should be attempting.