I would love to launch my project and wait (let's say 3 months) to see if it can actually make money. If it actually does, then I will register a business for it, otherwise, I would just shut it down.
Question is: is it legal to sell online services this way? Would you, as a potential customer, trust it? I'm based in Europe.
In the US it's legal, and is considered operating as a sole proprietor. But in doing so, there's no separation between you and the business, and you (and your personal assets) are 100% on the hook for any legal or liability issues that come up.
For that reason alone, I set up an LLC and route all consulting/moonlighting work and side projects through that LLC. The hassle and business licensing costs worked out as far cheaper than operating as a sole proprietor and getting the necessary insurance coverages to comfortably cover myself.
Although it depends on what your SaaS is, you may want to at least checkout a professional indemnity insurance policy[1].
[1] https://www.simplybusiness.co.uk/insurance/faq/what-is-profe...
Starting a limited business is separate. Then you need a separate bank account, register with the tax office, get a separate tax id. Depending on type of business you might need to bring in money (25.000 Euro for a German GmbH) or you need two founders. Year end taxes are more complex. Disolving a company is a pain.
VAT is also separate. Freelancers in Germany for example are exempt until 17.000 Euro, the limit is even higher in the UK.
So legally you probably need to register. Since you're already fully liable even when registered some people delay it, even months and then backdate. Not ideal but afaik there's no fine. I delayed by 5-6 months, tax office didn't care.
Individual customers won't notice, when is the last time you looked at the imprint of a website? (I do, but I might be the exception). B2B customers probably care. And larger account will already wonder "will this website still be online in 6 months" regardless.
I'd check with your local Tax Service first, though.
As for your customers: are you selling B2B or B2C? For B2C I wouldn't really care (in fact, there are a number of paid apps that I use that were made by private persons!). For B2C it could be a problem because your clients won't be able to deduct the VAT.
That is a question for a lawyer. Laws vary significantly between jurisdictions. These include tax laws as well as registration laws. If it is not worth paying a lawyer, it might not be worth pursuing as a business. Good luck.