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The usage of "ichi" (一) in names is definitely associated with a first-born, just as "ji"　(二) and "zou" (三) are used in names for second and third sons respectively. For example, Ken'ichi 健一, Kenji 健二. and Kenzou 健三, when written with these kanji, would be typical for first, second and third-borns. But whether or not "ichi" might also have an alternative or additional meaning of "putting something first" (or "the best at something"), I am not sure.　

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In any case, the use of numerals in names seems to have become much less common since families have become smaller.