Why give it a name then if it is purely abstract?

Because it is a very useful concept and deserves a name. What would you call
a decibel then? The unit formerly known as decibel? TUFKAD. Catchy. There
are other dimensionless units you would have to expunge, of course. Percent
(%) is a useful one that would have to go.

FWIW, my dictionary says it's a unit for measuring sound.

Your dictionary is wrong. It is used to measure power ratios (usually in
oscillatory systems of large dynamic range). Sound power is only one of the
measurements it is useful for. Amongst other things, it is also used to
measure vibrations and to compare electronic signals, not necessarily audio
in frequency or nature.

Christian.
BEng (Electronic and Electrical Engineering)