Agreed. Even if a relatively short description is possible ("complete normed vector space"), if a concept is used often enough, it might be named (in the case o

Agreed. Even if a relatively short description is possible ("complete normed vector space"), if a concept is used often enough, it might be named (in the case of the example, "Banach space") - what's the problem with that? In daily life, we don't say "Pull the horizontal surface suitable to sit on closer to the somewhat higher horizontal surface suitable to perform office tasks on", we say "Pull the chair closer to the desk", because we have given these concepts names.