Why does the Trinitarian Formula start with "In the NAME…" and not "In the NAMES…"?

Today the Universal Church celebrates the Solemnity of the Holy Trinity. In the Trinitarian Formula, we invoke the NAME (singular) of the Three Persons of the Trinity. In English we say: "In the NAME OF the Father, and OF the Son and OF the Holy Spirit." Note the repetition of the preposition 'OF' prefixed to each of the Three Persons, to reinforce individuality. But at the same time, we do not say: "In the NAMES of the Father, etc." Does it imply that there is but one name for all the Three Persons, and that Father, Son and Holy Spirit are not individual names? My question therefore, is: What according to Trinitarians is the reason for starting of the Trinitarian Formula with "In the name…" (singular) and not "In the names…" (plural)?