Pretty much everything in mathematics was named on discovery, which was usually before they understood what the concept they were discovering actually was. And, somethings even the name that was given is meaningless in English because it was given in a foreign language. Real Numbers aren't somehow special here.

There are a lot of elements in mathematics that arguably could be named better. Examples include (and obviously this is opinion, not a mathematician, in all humility, etc):

+ Negative numbers, real numbers, imaginary numbers, quaternion, etc (which should really all be named in a more systematic way) + sin, cos, tan (I doubt any link remains between the function and the concept in modern teaching) + Anything named after a person instead of named for what it is (eg, Euler's constant e; should have a more informative name) + plus, multiply, exponentiation, Knuth's up-arrow (a progression of the same concept, should be named systematically) + The assuredly long list of examples I don't know about

The gains don't justify the costs, but one suspects if you could somehow give an alien modern math theory without any of the name or symbol conventions they would invent a much more systemic system than hat we have grown.