Do I need to stay loyal to one Independent adjusting firm?

Not at all.  In fact, with very rare exceptions, no single adjusting agency will keep you busy all on their own.  In the U.S. alone, there are more than four dozen independent adjusting agencies.  Some are national and some work within specific regions only.  Each agency represents the claim interests of different insurance companies (the clients) and therefore no agency will be deploying adjusters to every storm that hits the country.  The industry recommends that each independent adjuster should join between 5 and 10 adjusting agencies just to keep active.  An excellent adjuster may join more.  Remember:  you can always turn down an assignment if you can't take it.  You may be already working claims for one firm when another calls to offer you a new assignment.  But put your name out there for as many opportunities as possible.  If it's a slow year, you want to be one of the adjusters out working and not hoping there's going to be a major catastrophe to provide you with the income you need.