Satsuki Azalea Cultivar Names

Is "Nikko no Hana" the same variety as just "Nikko"?

How about "Kozan no Hana" and "Kozan"?

Same for "Miyama Mangetsu" and "Mangetsu".

'Nikko no Hana' is a sport of 'Nikko'.

'Mangetsu' is a sport of 'Maiogi'.
'Miyama Mangetsu' is a kurume azalea from the Kirishima national park area of unknown origin.

'Kozan no Hana' I do not know.

Note, some 'Kozan no [x]' are sports of 'Kozan', others are seedlings of 'Kozan', again others have nothing to do with 'Kozan'.
Same can be true for 'Nikko' or 'Fuji' or 'Chiyo' or 'Sachi', etc.

Sometimes the Japanese name romanized may create ambiguity. There are two 'Reiko', two 'Shinsei', two 'Shinzan', two 'Tenshi', two 'Tensho', etc. There are like 10 more. Different Japanese characters, same romanization. Sometimes they can even have the same Japanese phonetic spelling.
It is just like Japanese personal names and their ambiguity; a phonetic name can be written with many different characters having different meanings.

Thanks! That's a very nice site you've got there!