In the Byzantine rite, the formula is “The servant of God, N., is baptized in the name of…” So, the words “I baptize” can be substituted for this and it would still be valid.
I think I see your point but that’s not really a literal translation. While there are no definite articles in Latin (no "the"s) you’ve got genitives there. So, you’ve got to throw in “of” before the Persons or somehow show possession.
To the OP: It is a good question. If he baptized “in the names” of God, then there would be more of an issue and I’d really doubt the validity. I don’t think that is what happened here so I’d agree with others and say it was valid since it still appears as though the priest baptized in the name of God. He “only” added superfluous words in two places. That being said, perhaps you could discuss the issue with him and see why he does this (if it is common for him) and say that you’d prefer that he uses the approved form, exactly. Since you know him pretty well and you say he is “extremely orthodox” he should receive your comments/questions with sincerity and understanding.
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