The idea of securing a domain name is to make it easy for users to find your business. In the day of social media, this extends far beyond the .com address and includes things such as facebook page address, twitter handle and instagram username.
It is best practice to keep everything the same. For example, our website is LoudMedia, this is also our registered business name. Because several social media platforms already had users with this username, we decided that it would be best to refer to everything as Loud Media Agency.
You should also try to secure as many variations as possible to your username.