Extremely silly.

Take, for example, OpenText. [1]

Nothing about it is free, or open source code, or in any other sense publicly accessible. [2]

I don't know if they operate in the EU, but I presume any application for a trademark would be rejected.

[1] https://en.wikipedia.org/wiki/OpenText

[2] It's "Open" as it turns paper documents into more easily accessible digital formats. But not public in any way.

The purpose of the company is also rarely defined by it's name. Brands aren't inherently descriptive and it's normal for companies to evolve over time.