Getting domain names, social accounts, and trademarks all falls under name registration.
domain name If possible, it's best to take a .com or you if you want to use a more common name then you might go for a different TLD like .net, .io, or .app for better name availability.
There are many domain name registrars available.
social accounts It's best to register any and all social accounts under the name you want to use, even if you don't plan to use them. It's better to avoid confusion in the future where someone has an account with your business name.
trademarks Note: This is not legal advice.
Go to the website of the patent or trademark office for any jurisdiction where you want to use the name legally for business. Check that someone else in the same category as you is not already using the name.
The big three patent offices are in the US, the European Union, and Japan
You will eventually want to register the trademark for any business or product you wish to sell, in order to prevent knockoffs or other parties that may confuse your stakeholders.
You can skip regstering a trademark for now, but you should use the name in writing as soon as possible to create a track record of "first use". This can be a key point in winning disputed trademarks, at least in the US.
Tip: You can add a modifying word like 'get' or 'go' to expand your options for domain names and social accounts, and then buy or acquire shorter ones later.