As a website designer, I would say it’s one of the main things you want to avoid. The site domain name MUST match the business name, no matter what. Even if you have to pay money to rename the business.
For a business, the domain must match the name, and it must be dot com. No exceptions.
When I see a site that has a domain that does not match the site name, I will always think negative things. such as “oh, they are a real small company that cant afford to buy-out their domain” or something such as “oh, this must not be the official site, i have come to the wrong place”
If you like, send me a private message with what you want to call your business, and ill give you a hand looking for a name. I have a fair bit of experience hunting down good names.