star trek - Why do aliens from the Delta Quadrant also refer to that part of the galaxy as 'Delta Quadrant'?

If I was living on a planet somewhere in the galaxy and decided to divide that galaxy into some named parts, I would probably name my own region the 'Alpha' part, and chances are that not all species divide it in exactly 4 parts.

In several Voyager episodes, Delta Quadrant aliens either call the region the 'Delta quadrant' themselves (I think this was in VOY5x10 Counterpoint)or seem to naturally understand what it means when some of our Voyager heroes say it. Is that the Universal Translator doing a very good job? But if so, how could it know if those aliens divided the galaxy into 4, 7 or 29 parts?

Or are we to assume that the Voyager crew (offscreen) explained the Federation way of quadrants to the aliens?

Or (out of universe) didn't the writers think this through?