a name: the word by which a person, place, or thing is identified, which in the New Testament regularly stands for the person's whole self, their authority, and their publicly known standing.
In Greek as in Hebrew, a name is rarely just a tag. It represents the person who bears it, which means that to speak, act, pray, or trust in someone's name is to deal with that person themselves, invoking their authority and presence. That one insight unlocks most of what the New Testament does with this word.
The practical naming uses are what one would expect: a priest is called Zechariah, an angel names the child to be born, a man in the Gerasene tombs says his name is Legion, and lists of the apostles record their names. At this level the word is transparent: it simply identifies.
The deeper and more theologically freighted use is the cluster of expressions built around acting or trusting in someone's name. Baptizing into the name of Jesus, praying in his name, gathering in his name, receiving someone in his name, performing deeds in his name, and believing in his name all rest on the same logic: the name stands for the whole person and his authority, so these actions are being done in relation to, under the power of, and in alignment with the person himself. This is especially concentrated in the Johannine writings, where Jesus tells his disciples to pray in his name and promises that the Father will send the Spirit in his name.
A third range covers the name as a person's publicly recognized standing: the name that is exalted, inherited, or profaned, the name that is blasphemed among the nations, the name above every name that God gave to the exalted Christ. Here the name is something more like honor and distinction, the worth that others recognize in a person.