newbie questions about PayPal/starting website business

Hi, I would like to buy a beginner's website on flippa, and try to make it work. A couple of questions: I don't want to register it as a business, or even do a DBA (doing business as) until I see if I can make any money at all doing this! Even once it is hopefully up and running, it would probably make a few hundred dollars a month. Can I treat this as a personal hobby for a couple of months until I see if I can make a go of it? I want to buy a small website that sells packages doing SEO services or similar, and I outsource the services to a provider abroad. Legally, can I just open a PayPal Premium account and receive and send money for this website as a sole trader? Because it is weird to actually get a business license and DBA for something that might not earn any money at all, so far this is just an experiment.

Also, is there any way to receive payments on PayPal showing the website's name, or does PayPal Premium always only show my personal name? The email address would be in the website's name. What exactly appears when customers send payments to a PayPal Premium account? Because I would strongly prefer to not have my own name appear.

Also, I am thinking that initially I would just open a normal but separate checking account and credit card specially for this website, so as not to mix any other monies with this website. Would this be sufficient--as I would not yet be a business? I understand that you cannot get a business account without a DBA and EIN.

Of course, if this should start earning money, I would immediately get a DBA and if necessary any business licenses, and would upgrade to PayPal Business account and a business checking account.

Would greatly appreciate any advice as to how to initially set this up, and how to start this Internet business. Thank you!