As a general rule, you should validate is the name or a substantially similar name is not being used anywhere for a business in a related field. So, you want to look for more than just a trademark in more locations than just BVI. To start, you begin with extensive searching for your name or similar names on Google. If there is no competition in a similar space, then, the largest database of corporate names is in Delaware, so this is a good place to start to see if there is a business entity with a similar name. Lastly, if everything is clear, then you do a trademark search.

The link to search in Delaware is:

https://icis.corp.delaware.gov/Ecorp/NameReserv/NameReservation.aspx