Read the TOS (Terms of Service) for each DNA service you are considering. Each service will clearly outline the privacy of submitted samples, security of the process of analysis of samples, the storage and distribution (and possible destruction) of the resulting data, and linking of personal names (or the granting of anonymity, if available) to the data. The TOS will give you enough information to determine if you are comfortable with the privacy of the service.
The TOS is a legal document; both you and the service are bound by that contract once you submit a sample and pay the fee. The TOS may outline any legal recourse you have against the company for violating the TOS.
Each service is bound by the laws of the country where it is located and the countries where it might outsource the analysis, as well as relevant EU law - since you're looking at EU based-services - to provide security and privacy. Those laws will be outlined in the TOS.
As an example, read https://dna.ancestry.com/en/legal/us/privacyStatement at ancestry.com about their DNA testing. It's an extensive TOS, and outlines US and EU law, including the Swiss Safe Harbor Framework https://en.wikipedia.org/wiki/International_Safe_Harbor_Privacy_Principles
The DNA service, of course, can't guarantee the security of the data - or your personal information - in perpetuity. Companies are sold, TOS documents change (which would have to be subsequently approved by you), data storage systems "leak" information (by insiders and hackers), and on and on.
...but I don't mind doing a lot of research on my own to classify it
if I get raw results.
And, any kind of site that allows you to compare your DNA profile with others - if it is a different site/service than one that does the DNA analysis - will have its own TOS regarding the privacy of your data and the resulting metadata from comparisons to other DNA profiles.