Given that we’re in 2016 there is a very good chance that your business name might be taken (or the domain, twitter handle, or even page address on Facebook) or that someone else had the same cool idea as you.
But that doesn’t mean you shouldn’t pursue your dream! There is always room in the market for more.
Yes it does mean that you may be harder to find in the crowd, so its important that you stand out in your own special way (which won’t be too hard given than most VAs are so ‘vanilla’ and don’t try and differentiate themselves in any way).
My advice? If you’re serious and passionate give it a good hard go! Get help and guidance if you need it and have fun 🙂