I believe that “In nomine Patri” is a case of the Dative of Possession. I could argue for “Spiritu” as another dative, based on an entry in Bennett, “New Latin Grammar” (1908), section 49.2. [Bolchazy-Carducci reprinted this volume.] But that would dictate “Spiritu Sancto” in order to create agreement, and while many formulations may have been used (“Fili” can also be correct ~ Bennett 25.2), this does not seem to be one of them.
I have seen Niermeyer’s Medieval Latin Dictionary in what I assume was an unabridged form, and it seemed like a thing of beauty to me. I had not heard of Stelten’s “Dictionary of Ecclesiastical Latin” until I started to research this answer.
Anyone up for a discussion of whether the “doulos” (a transliteration from Greek) of the high priest whose ear is struck off in the Garden of Gethsemane, then reattached by Jesus, is a really slave or, as it is often translated, a “servant”? [My bias shows in the quote marks.] My Attic Greek dictionary (Liddell and Scott, abridged) does not permit “slave” as a translation. I don’t have access to a copy of the Bauer Lexicon, the great resource on biblical Greek.
The Vulgate (about 400 AD) uses “servus”. The Golden and Silver Age of Latin Literature (ending about 100 AD), as documented by Charlton Lewis’s great dictionary, permits both translations, but “slave” appears first. Niermeyer, cited above, covers 500-1150 AD (I think), and encourages “servant”.
Even by the time “servus” has become “serf” in the Russia of the 1800s, “servant” is not an acceptable translation. I believe that this translation appears so often because translators are not comfortable with the ethical situation in the original text. The NRSV uses “slave”, and the HarperCollins Study Bible of this translation does not seem to feel that the choice is worthy of a footnote.