Adeena means "Friday" in Arabic slang, this is not found anywhere in the standard dictionaries.
`Adeena is also the ancient name for the city of Ta'izz in Yemen.
`Adeena is also an ancient word that means the goods that are stored in large jars.
Adeena could also be the plural of deen (religion, creed), thus it would mean "religions, creeds". This is not a standard plural (the standard is diyanaat), and some or most people may consider it wrong.
Both of Adeena and `Adeena (the second one starts with the letter ain, as in alaikumassalam) are extremely rare names in Arabic. But you can use them, and both actually derive form Quranic roots, deen and adan (adan is also the root for the Arabic word for Eden), for this reason they can be considered indirect Quranic names.