Can I use a business name that is already in use by simply adding "LLC" or another word to the end? Thanks!!

There are two levels to your inquiry - one is what the state will allow as far as registering a name, and the other is a broader question as to whether you are violating someone else's trademark. As to the first question, the SOS will not let you register an exact name that has already been taken, simply by adding LLC, Inc., or the like.It probably will let you register a modified version, such as Arrowhead Brand in your example. However, by accepting the registration, the SOS is not offering any opinion as to whether you might be violating someone else's trademark. Trademark/tradename issues are quite a bit more complicated, and I recommend you consult with a trademark attorney if you have concerns that your business name, however it is used, could be seen by another company as a violation of their tradename. Thus, in the Arrowhead example, if you used Arrowhead Brand, and opened a business that does hosts social or sporting events, you would probably have a problem with the Arrowhead Gold Course.

The "extension" is largely irrelevant. Adding the Inc., LLC, Ltd. etc. doesn't alter the core issue. Someone is already using the name. You need to change the name more than just by adding the corporate extension. Then, an analysis must be done to determine if your business "operation" (that is, what your business does), conflicts with the current name holders business. Let's take your example. Assuming the existing company "Arrowhead" is not in the clothing business (and assuming you are), you could probably have the business name Arrowhead Wear, that would likely be okay. However, then turning around and using "Arrowhead" as, essentially, a trade name may be problematic. In reality, what you call your business entity is the lesser of the two issues. The more important issue is how you portray yourself in the marketplace. What you call your LLC is largely irrelevant. It wouldn't cost you a ton of money to sit down with an attorney and vet the issue. You don't know how aggressive other users of the name may be in defending their trademark, so a penny worth of prevention now is definitely better than a pound of cure later.

You cannot distinguish your business merely by adding LLC. You can add another word or phrase to distinguish it if that combination is available. And just because it is available as a business name does not mean it is also available as a trademark.