Name (Grk. onoma) certainly carries the meaning of authority but by metonymy can also mean "person". In Matthew 28:19 where we find "in the name..." we have the Greek preposition eis , literally "into", rather than the preposition en, "in"). The scriptures inform us we are baptized "into" Christ so it seems to make sense that onoma refers to "person" rather than "authority".We tend to read Matthew 2819 as current Americans with the assumption of the word ‘name’. It carries with it the description or meaning of authority, and therefore is not a proof text for the trinity like many assume.
People may then reply and say that only a person has authority, however the constitution has authority for one example the presence of a person via representation carries the authority.