Re: When registering your business name...
I'd register the whole thing, then refer to the business in whatever shorthand way makes sense. Actually, that's what I really did. My name is legally "Sunny Words Writing Services," and that's what my license and tax forms say, but my domain name, site text, checks I receive, mailbox account, etc. all usually just say "Sunny Words." I guess it's roughly equal to being legally named with a first and last name but commonly going by just your first name.
That said, if you're planning to register as a corporation rather than an IC, you may need to follow somewhat different rules. When the time comes to register, if your locality has specific regulations about how you refer to yourself legally, they'll tell you.
As for "virtual," that's completely up to you. If you want to emphasize it, by all means do so. But there's no rule I'm aware of that says you must/must not.
I'd guess you actually have a lot more choice in the naming matter than you expect--which is a good thing. Yay for autonomy!
I wish you smooth sailing in all your preparations!
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