If you look at the trends, most companies leave the ".com" out of their business registration. It's pretty unnecessary and makes your name longer and more complicated, which in most cases is not super appealing, in my opinion. Also, consider whether your firm will branch out "offline" in the future, because at that point the argument for a ".com" name extension loses some weight.
In the end, there is no "rule" for this, it is not at all important, and won't have a great impact on your business. Go with what sounds good.
My humble opinion on the subject.
.com is a technical internet detail. When it was considered cool to have "online presence" (and that being special died around 1999) people loved to add a ".com" to their official names for some wow factor. It's still around with those companies: "Amazon.com, LLC" etc.
Today however, people don't "wow" at .com anymore. They do ridicule companies who are not on the internet, but I'd say. call your company XXXXXX, LLC and simply have a domain called XXXXXX.com.
you could also go with registering a ".com" business if you like the sound of .com with your company name (like say, match.com) It's really up to you.