@robert1849 If the source bank is on the "good" register, then yes if the name of the sending account is the same as the destination account, usually that raises no red flags if the value is below €10k.
In the past when transferring €30k between accounts both in my name, I've had the transaction stopped because they wanted proof of source of funds i.e. from where did I originally get that money?
Proving that can be hassle, like digging up wills to prove it came from inheritance etc. But what else can you do in the end?
Something a lot of people aren't aware of is within the EU financial information is automatically shared with all EU tax authorities. Every account you have the balance is shared at least every month, sometimes daily. Most EU countries have a similar financial information swapping agreement with the USA with their tax authorities. Basically you need to assume if you live in the OECD, all the OECD tax authorities can see all your financial data on a monthly or better resolution.
Also, in some countries it is legal to sell your financial transaction information to a central register, where it can be resold onto commercial buyers. Political parties will buy that data, and use it to target you for votes and other things. In EU countries it's supposed to be "anonymised", but from other data sources you can buy e.g. card purchase history or mobile phone location history it's possible to deconstruct which household with a good accuracy. All that is automated by commercial data providers, if you're willing to pay you'd be amazed at the fidelity of "estimated" information about people you can buy, even in the EU.
Despite all that, the EU is rife with financial crime, mainly VAT fraud for business and scams for individuals. That's mainly because the powers that be don't actually care about individuals that much. They only care about groups, particularly ones who control swing voting blocks such as the elderly. And the VAT fraud, that they do care about a lot, but not enough for each country to give up their exclusive control over their VAT system. So tens of billions gets defrauded every year, and nobody will do anything about it not because they can't, but because they don't want to.