You can take inspiration from the function of a website and create something that functions similarly – assuming that you don't copy the graphic design. You also can't just copy their code used to create the outputs, but you can reinvent that wheel.
In some cases, the underlying real facts could be assembled by the sweat of the brow, as you might get from a digital Norwegian phone book, or from the list of approved names (a government document). It is not possible to generate exactly what the webpage generates without copying the (protected) code – the data is part of the code. Not everything generated by the website is a "fact", for example the Central Asian town name generator is based on a creative rule of the author's invention, and the "Central Asian town" Torakol is not a real fact, it is a creative invention.
I conclude that with a lot of effort, you could legally construct code that functions like the original page does, and does not copy its embedded databases. But you would have to create your own databases, and therefore the results would be different (example: Ashon is not a Swahili name, the author may have scraped a baby-name website and simply installed the original error in the code, knowingly or unknowingly).