Buurtbieb - in English, roughly pronounced as b-eew-rt-beep.

It's a literal translation of "neighbourhood library", it alliterates, and it sounds cute. (Keep the "beep" part short for that).

Just keep using it as a generic name. They've already lost the generification war. Are they seriously going to track down and sue neighborhood libraries?

Good luck getting a jury to enforce the trademark.

It seems bizarre to me that someone could trademark such a straightforwardly descriptive name.