"sending away demons." This refers to casting demons out of people. Alternate translation: "driving demons out of people" (See: [[rc://en/ta/man/translate/figs-explicit]])
Here "name" is associated with Jesus's authority and power. Alternate translation: "by the authority of your name" or "by the power of your name" (See: [[rc://en/ta/man/translate/figs-metonymy]])
This means that he is not among their group of disciples. Alternate translation: "he is not one of us" or "he does not walk with us" (See: [[rc://en/ta/man/translate/figs-idiom]])