How does one say "telephone number"? telefona numero?

On the one hand your translation seems logical, since telephone sort of becomes an adjective in that instance, describing the noun number. On the other hand, I notice the translation for "Telephone book" is "telefonlibro" which is just a combination of the two nouns "telephone" and "book" ran together.. rather than telephone turning into an adjective.

But I was wondering about "telephone number" myself though, if there was a more "official" translation.

good point

I say telefonnumero.  Telefononumero, or telefon-numero or telefono-numero would likewise be grammatically correct, but I've always heard it and seen it written 'telefonnumero' without exception so far.