If you are planning to start a business or you plan on changing the name of your existing business, you want first of all to check that there are no other businesses with that name with whom you are likely to conflict. After all, you want to have your unique brand available so that you can create a marketing plan around it. You would not want to create your brand and then have another company steal your clients! It would be sensible therefore to be able to make a search to see what other businesses are operating under your planned name before beginning the process. You want to be able to search for companies, you want to check domain names and social media handles.
In order to verify your business name online, one way would be to go through the process of checking each of the areas individually, which is obviously going to be somewhat time consuming, but perfectly possible.
Corporations should be registered and you will be able to check this in your state department website by conducting a LLC name search. Remember that not every company will choose to register, some may prefer to wait until they are caught out. It is also worth remembering that sole traders do not need to register, so an internet search may provide you with something.
If you are planning to start your new business in the US, it would be worth checking to see if your business name has been trademarked by someone else. You can do this by checking the database for trademarked names by making a search with the U.S. Patent and Trademark Office.
You can search and find a company who specialise in domain name registration, there are a number of companies who do this, then follow the instructions to make a search.
You will have to decide on which of the platforms that you intend to use and then go about checking with each one.
You should make a point of searching through all of the search engines using the names that you are planning for your company. This should provide you with some interesting results as you may or may not find companies with the same name but what can happen is that you find a company with a very similar name and it may be that that would create enough of a conflict for you to consider something else.