I guess it’s a little different when you’re talking about pseudonyms, but I wouldn’t go anywhere near trying to come up with a kanji name, personally. I really don’t think you’re asking this in the right place, though – TextFugu is for new learners, pretty much. You want native speakers, so maybe ask at Lang8 or Hinative. (Was gonna add “besides, how often do you come across someone named Law in English?” and then I went “oh yeah… Jude Law”. =P )
That said, how do you figure 認 is read as みとむ? Near as I can tell, the only nanori it has is みとめ, but maybe I’m just looking in the wrong place.