The "heart" refers to the deepest thoughts and desires of a person. AT: "thinking about individually" or "considering in their private thoughts" (See: [[rc://en/ta/man/translate/figs-metonymy]])
# in my name
This refers to a person doing something as a representative of Jesus. AT: "because of me" (See: [[rc://en/ta/man/translate/figs-metonymy]])