Do you prefer <your_full_name>.<tld> or <your_pseudonym>.<tld>?
I feel a bit uncomfortable using my full name to receive email, what do most do?
Well, first, most people don't have either the desire or the power to name a domain after themselves. Don't you mean the "user" part of an e-mail address, like this:
user@domain.com
To answer your question now rephrased, I think it depends on whether you intend to accept responsibility for what you post. It's my experience that young people prefer anonymous "handles", but as one becomes older, the advantage of posting under your own name becomes more obvious.
> This came up when I was trying to setup my own domain for receiving email.
A domain just to receive e-mail? Okay, now I feel out-of-date. There was a time when a simple e-mail address served that purpose, say from Gmail. A Gmail account is free and it can be set up to forward to a secondary email address, so you don't even have to visit your Gmail account if you don't want.
I am an amateur musician by night. I spread my music only with pseudonym and send only e-mail by pseudonym.
Not sure what kind of e-mails you are going to send. But if you want to make business (and this business is not upsetting anybody basically) I would go with real name. If you do want to make art, I would prefer pseudonym. I actually have had problems in my day job in times when i published art with real name.