The word "Happy" is English and the word "Hanukkah" is Hebrew.
Happy Hanukkah= Boldog Hanukka
Just like this: Happy Hanukkah
There is no such thing as "Hebrew Orthodox". There is only Hebrew. In Hebrew, you usually do not mention the name of the holiday in greetings. So you would just say Happy Holiday, which is hahg same'akh (חג שמח) Some communities do say Hanukkah Same'akh (חנוּכה שמח) meaning "Happy Hanukkah".
Words that can be made from the letters in Happy Hanukkah are:aahahaanankhanyaukayahhahahhankhankyhaphayhuhhunkhunkyhuphyphakahunakappakayakkhankhaphknapnahnapnappynaynupapahpanpappapapapayapaypukkapunpunkpunkahpunypuppupapyauhunhappyupyakyankyapyaupyuanyukyup
Hanukkah is the name of Hanukkah. In Hebrew it is spelled חֲנֻכָּה
the traditional greeting is Chag Sameach (?? ???).
Happy Hanukkah = Hau'oli Hanuka
Hebrew.
Hanukkah always starts on the Hebrew calendar date of 25 Kislev
"... and Happy Hanukkah!"
"Happy Chanukah" or "Chag Chanukah Sameach"