Onoma May Sometimes Mean Authority

ONOMA spoken about in Mt. 28:19 evidently does not refer to a rigid designator such as YHWH. Rather, ONOMA in this instance evidently signifies "authority":

"The name of Jesus is the essential part of it [the
Matthean formula] as is shown in the Acts. Trine
immersion is not taught as the Greek Church holds and
practices, baptism in the name of the Father, then of
the Son, then of the Holy Spirit. The use of name
(ONOMA) here is a common one in the Septuagint and the
papyri for power or authority" (Robertson's Word
Pictures).

Moulton-Milligan supplements Robertson's comments:

"The [papyrological] usage [of EIS ONOMA] is of
interest in connexion with Mt 28:19, where the meaning
would seem to be 'baptized into the possession of the
Father, etc'" (page 451).

M-M acknowledge the meaning "office" or authority for ONOMA too.

See Mt. 6:9