If you look up the etymology of the English word 'name', you'll probably find it given a Germanic or Old English origin, but its roots go much deeper, to the proto-Indo-European no-men-.
No-men-, in turn, gives us everything from the Sanskrit nama, to the Latin nomen, to the Greek /ὄνομα.
Ὄνομα has been used from Homer down, and is still in use (without the breathingmark) today. It is a third-declension neuter, and the declension is as follows:
nom. ὄνομα nom. ὀνόματα
gen. ὀνόματος gen. ὀνομάτων
dat. ὀνόματι dat. ὀνόμασι(ν)
acc. ὄνομα acc. ὀνόματα
It's a common noun, with about 230 uses in the New Testament. Most of the forms above are found, but there doesn't seem to be any instance of the dative plural, ὀνομάσι(ν). We saw the genitive plural όνομάτων in Acts 1:15.
It can almost always be translated with the English 'name', and is used in phrases where someone or something is given a proper name, e.g.:
καλέσουσιν τὸ ὄνομα αὐτοῦ Ἐμμανουήλ
they will call him Immanuel (Matthew 1:23)
There are common uses of ὄνομα with the prepositions εἰς, ἐπί, and ἐν, which might be usefully memorized:
1 εἰς plus accusative; 'in the name of'
εἰς τὸ ὄνομα τοῦ κυρίου Ἰησοῦ
in the name of the Lord Jesus (Acts 8:16)
2 ἐπί plus the dative; 'in the name of', 'in [someone's] name'
πολλοὶ ἐλεύσονται ἐπὶ τῷ ὀνόματί μου
many will come in my name (Mark 13:6)
3 ἐν plus the dative; 'in the name of', 'in [someone's] name'
καὶ τὰ δαιμόνια ὑποτάσσεται ἡμῖν ἐν τῷ ὀνόματί σου
even the demons submit to us in your name (Luke 10:17)
The dative of ὄνομα can also be used without a preposition, to mean approximately the same in ('in the name of'):
οὐ τῷ σῷ ὀνόματι ἐπροφητεύσαμεν
did we not prophecy in your name? (Matthew 7:22)
Next time - back to Acts.