Yesterday we discussed how the word nun נון can mean "fish" in Semitic languages. Stahl writes that there are those that say that the word tanin תנין is related to the word nun. In the Tanach the tanin clearly refers to more than one type of animal, and not all experts agree in every case which one. Kaddari writes that the tanin is a snake (Shmot 7:9, together with Shmot 4:3), crocodile (Yechezkel 29:3 - here tanim תנים, this is the meaning in modern Hebrew), viper (Tehillim 91:13), leviathan (Yeshayahu 27:1). Of course the identity of the leviathan is also not clear, and from here we get the tanin translated as "giant fish" (Rashi on Bereshit 1:21), whale, and the general "sea monster". (For an interesting article on the significance of the mention of the creation of the tanin, go here.)
Klein does not connect tanin with the word nun, but rather with a root תנן , which has cognates in a number of Semitic languages - such as the Ugaritic tnn , meaning "dragon".
However, both Stahl and Klein mention a theory that the Greek word thynnos was borrowed from the Hebrew tanin. From the Greek came the Latin thunnus - and from here the English words tuna and tunny. (Tuna is actually much more recent than tunny, and entered American English via Spanish, and the Spanish was borrowed from Arabic, which took the word from Latin.)