During the trip to Nepenthe, Hiccup, Toothless, and the rest of the Dragon Riders encountered a large group of sea dragons, two of whom were Soaky and Wetty. The Riders found out that the sea dragons wanted to give Toothless, the Alpha, an escort to Nepenthe. Realizing that the dragons were friendly, Ruffnut and Tuffunut jumped off of Barf and Belch and on to Soaky and Wetty, enjoying the ride on the two Seashockers. After a period of time, the twins reboarded Barf and Belch and Soaky and Wetty continued with the escort. Barf and Belch were still angry about this on Nepenthe. The twins, however, state that "Soaky and Wetty wouldn't hold a grudge," thus giving them their names.
Despite both being two-headed dragons, Soaky and Wetty both seem to only have one name, rather than each individual head having a name.