Aye, you really never need to admit to living in a van, unless you are being questioned with probable cause
Even when applying for work, they don't need to know. Give them a fake address, show up clean, nothing to it
You can get a physical address through a mail forwarding service like Escapees dot com, iPostal1, or Mail Messages and More.
Make sure you understand the difference between domicile and just mail before your tags expire. There's good info at escapees even if you don't choose to domicile in Texas, Florida, or South Dakota.
You have decided to take time out of your busy schedule to go camping and explore America. The bureau of land management and forest service offer many campgrounds, some with amenities such as vault toilets, garbage, and even water, where you can stay for free for up to 14 days.
You have the right to pull over at a rest stop, truck stop, or other safe place to sleep. This is for the safety of everyone on the road. You have researched the laws in the states you are passing through.
You generally try to follow the 3-3-3 rule: don't drive more than 300 miles in a day, more than 3 hours without a break, and plan on getting to your campsite by 3 PM so you have time to set up before dinner.
Other campers may ask if you are a part timer or a fulltimer, but as far as the locals are concerned, you are what is known as a "tourist".
You are good for their economy.
Try to buy local and be prepared to talk about the weather in the state where you are domiciled.