From what I can find on
www.myojiyurai.net and
www.douseidoumei.net (latter uses data from telephone books hence the lower numbers), Mitose is, unlike Suzuki or Katō, a rare surname.
Two variants of this surname can be written, either as 水戸瀬 (the more often used variant) or 三戸瀬. Coincidentally, while the first two kanji of the more often used variant is the same one used as for the city and former domain in what is now Ibaraki Prefecture, the majority of those who have 水戸瀬 as their surname live in Akita Prefecture according to both of the sources above.
To see what each of these kanji mean: please see
http://jisho.org/search/%E6%B0%B4%E4%B8%89%E6%88%B8%E7%80%AC%20%23kanji
My PNL:
http://www.behindthename.com/pnl/149249My blog:
https://maybeitisdaijirou.wordpress.com