Phonetic mapping: 阿 (ā, 'a') + 迈 (mài, 'ma') + 瑞 (ruì, 'ri/ry'). The 阿 prefix is often used at the start of transliterated names beginning with vowel-A sounds (compare 阿曼 'Oman', 阿姆斯特朗 'Armstrong').
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瑞 (ruì) means 'auspicious' — a flattering character commonly chosen for transliterations where the 'r' sound needs covering. The same character appears in 瑞士 ('Switzerland') and 祥瑞 ('auspicious omen'), making it easy to remember.