From Japanese 歩 (ayu) meaning “walk, step” and 夢 (mu) meaning “dream, vision”. It can also be written with 歩 alone, or with other combinations of kanji.
From Japanese 歩 (ayumi) meaning “walk, step”. It can also be from 亜 (a) meaning “second, Asia” combined with 由 (yu) meaning “reason, cause” and 美 (mi) meaning “beautiful”. Otherwise it can be written with different combinations of kanji, or with the hiragana writing system.