According to the YoYo Games website, the name “Game Maker” is a registered trademark, denoted by the (TM) symbol beside it on their website.
I am not one to speak for English or Netherlands’s law system (wherever the company is now said to be located).. however, what I do know is that in most western living style countries (Canada, USA, Australia etc.), it is no longer possible (if ever possible) to register a trademark for a phrase of non-innovative words in regular English that describe a product or service.
For example, you cannot register a trademark for “Food Chiller”, “Wood Carver”, “Screen Cleaner”, “Game Maker”, “Foldable Chair”, “Chocolate Peanuts” etc. because these are all short descriptive phrases using common words that have no special meaning, and no extraordinary significance.
At this point, even if the company was able to find a copyright/trademark or lawyer’s office that would issue a registered trademark certificate for the “Game Maker” name, it would be no use, since it would never stand up in court.
The judge would see that there are many other programs out there called “Gamemaker”, “GameMaker”, “Game Builder”, and probably even “Game Maker” and this would indicate to him or her that the name had no particular innovation if he/she hadn’t realized that already. That is enough grounds to dismiss the claim and trademark.
I speak from experience, a company I was involved in, semi-recently had a legal dispute over a couple of trademarks they owned. Despite having the actual trademark certificates and such, the trademarks were dismissed and seen as irrelevant in court. To give an example, I believe one of them was “Ice Chiller”.