>>35812722>>35812806>ライ Rai (雷 thunder)>エン En (炎 fire)>スイ Sui (水 water)In the final their names are direct transliterations of their final Japanese names (as IIRC all legendary's names are from Gen II onward) but I don't think that would have happened with names that are so short and kind of awkward for English-speakers.
Expanding the name while keeping it plainly Japanese and retaining the theme/intent, I think the best option would be adding "-jin" (神 god/kami) to their names, making them Raijin, Enjin, and Suijin. Raijin and Suijin are proper Shinto deities (the gods of thunder/lightning and water respectively) and also used as general terms for lesser related kami, "Enjin" isn't a proper term but I don't think it's blatantly incorrect Japanese either, and in English it works as a nice pun on "Engine"
Alternatively it could go more literally and add "-inu" (イヌ dog) to their names, making them Rainu (ライヌ), Enu (エンヌ) and Suinu (スイヌ). That sounds more awkward, though.