So what?
There is only one "name" referenced.
With 3 possessives, that is just not the case.
"In the name of" is indeed an invocation of authority.
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But εἰς τὸ ὄνομα means "into the name", not "in the name". [This is what the Greek says]. So what does baptize/immerse
into the name of such a thing and of such a thing and of such a thing mean?
Strong's G1519 - eis
εἰς eis, ice; a primary preposition; to or into (indicating the point reached or entered), of place, time, or (figuratively) purpose (result, etc.); also in adverbial phrases:—(abundant-)ly, against, among, as, at, (back-)ward, before, by, concerning, + continual, + far more exceeding, for (intent, purpose), fore, + forth, in (among, at, unto, -so much that, -to), to the intent that, + of one mind, + never, of, (up-)on, + perish, + set at one again, (so) that, therefore(-unto), throughout, til, to (be, the end, -ward), (here-)until(-to), …ward, (where-)fore, with.