Changing ANY of your contact information is not good business. Even if it is just a fax number. Without a solid contact info that rarely changes, you could be seen as "fly-by-night" and not worth the risk. You should only change your contact info for good reason: permanent move to a rented/owned office space outside your home, permanent move to another city/state, adding phone & fax lines. This is not just nursing, this is a business. Without following business rules you may not have a business to run.
Don't forget, there is more than just personal income tax when you run a business. You will be paying "self-employment" tax BEFORE you make money based on previous quarter's or year's income. There are also other taxes that may be assessed by different localities for business taxes. They take that stuff pretty seriously and do not want you operating out of other locales. Otherwise the county and/or state that you filed for business operation in will lose out on local taxes as well as the county/state that you are in could be owed taxes an you didn't know it. They tend to frown on not registering in the county/state that you will be in and 3 months at a time could constitute an office address move. If someone wanted to push the issue, you could be in trouble for not maintaining a an address in one place and thus not paying business taxes. And every county and state has different rules on taxes, filing for business permit, etc. Unless you are well versed in all the rules of finance and taxes, I recommend you get a CPA to keep yourself out of trouble with the government.
Since marketing is one of the most important aspects of getting work, moving frequently would decrease your ability to effectively market in one area. Often times it is harder to say no to someone that is in your face in person. But it is really easy to hang up the phone or throw marketing materials in the trash. Always moving around would hinder your ability to market to the same people. It can take 20 or more contacts with you or your ads before someone is willing to buy from you. You will not be able to provide consistent contact to the same people if you are never in the same place.