How can 蛙 be read as あ ("a") in Asui Tsuyu's name? In Japanese, Asui Tsuyu's name is written as 蛙吹 梅雨. Most of the kanji in her name makes sense. 梅雨 is read as つゆ ("tsuyu"), and 吹 is read as すい ("sui"), but from what I know 蛙 is read primarily as かえる ("kaeru"), and can also be read as かわず ("kawazu") or かいる ("kairu"), but I can't find anything about reading it as "a". Moreover, it isn't a jōyō kanji or a jinmeiyō kanji, so I find it unlikely that it's something that happens when the kanji is used in names, as it generally shouldn't be used in names at all. So what's the deal?
蛙 has ア【a】 as one of the on-yomi, and kanji compound is usually read in on-yomi (some also have a reading in kun-yomi, but in general, all of the kanji in the kanji compound are read in either kun-yomi only or on-yomi only, but not mixed).

Some example where 蛙 is read as "a":


  
  蛙黽 (abou): tree frog (toad)
  蛙鳴 (amei): frog calling​
  蛙鳴蝉噪 (ameisensou): annoying noise; fruitless argument; useless controversy
  


As for Asui, her kanji representation 蛙吹 is read in on-yomi as 蛙（ア） and 吹（スイ）