Indeed. I hope the name is somehow related to Matrix, however, so that the connection is a bit more obvious. Perhaps Transform or Neo.
There are decent terms in the screenplay of the Matrix movie to draw from.
Despite nobody being able to spell most of them, the ship names would be good. Nebuchadnezzar, Logos, Icarus etc.[0]
There’s also other terms such as “construct” (the local Matrix instance /site before you enter the real matrix)
Only 2 problems in computer science I guess.