If i want to say the du’aa' of Yoonus, peace be upon him (la ilaaha illa anta subhaanaka inni kuntu minaththaalimeen), must I first mention the name of Allaah? Because if i don’t, then it sounds like it doesn’t make sense if i only say “there is no deity except You” because who is you? I didn’t clarify beforehand

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

You do not have to say the name of Allah first, and the pronoun "You" definitely refers to Allah Almighty because the speech is addressed to Him, Glorified be He, and not to others.

So you should say the supplication without any addition.

Allah Knows best.