Your brain is the squishy jelly between your ears.
Your mind is what disappears when that jelly gets shaken too hard by a punch.
Since a brain can exist without a mind, why not a mind without a brain?
Exomind — an individual's PIMS and the personal info it contains. One can wax philosophical about how far the exomind extends into situated cognition. Perhaps the Internet is a shared global exomind. Anyway, Cyborganize is a personal exomind.
Brain–computer interface (BCI) - a direct communication pathway between an enhanced or wired brain and an external device.
Exobrain - the external device that a BCI connects to
Second brain — a misnomer popularized by Tiago Forte's brand, intended to be synonymous with exomind. Bound for obsolescence once real second brains exist, whether wetware or hardware. I'd call the term overcrowded, but two of its three meanings are errors, leaving "gut brain" the winner.