UK you can be a sole trader, basically a person acting as a business. I believe there are some rules about how you legally present yourself (like in your contracts your name has to be "Bob Smith trading as Acme Widgets").
However, as the page says, you're personally liable if something went seriously wrong.
The alternative is to pay £50 to register as a ltd company, though there are costs in running one (£12.50 per year + doing your own accounts vs paying an accountant £200-£300).
In the US you can use a fictitious name dba "doing business as" name. You can also open up a bank account using a dba name. You may need to file taxes as a sole proprietor.
In the Netherlands, there is a threshold, and you do not have to incorporate if you stay under that, and you'll still have to report it. But this obviously depends on the country you're in.
Paypal could be a good way to take money from people privately, and it's probably entirely legal, up to a certain point.
Not sure how general this is, but in Poland if you have SaaS you need to have a company (because it's a "service"). But when you are selling just source code to someone else, it can be counted as personal income (no company needed).
https://www.gov.uk/set-up-sole-trader
However, as the page says, you're personally liable if something went seriously wrong.
The alternative is to pay £50 to register as a ltd company, though there are costs in running one (£12.50 per year + doing your own accounts vs paying an accountant £200-£300).