Spock doesn't merge with brains - his fingers barely touch the skin (or other shell) of the other half in the conversation!
Instead, Spock apparently taps into some sort of emissions from the chat partner, at a distance of several centimeters in the case of mind melds, at a distance of thousands of lightyears in the case of strong emotions expressed simultaneously by hundreds or millions of individuals. Different beings send different emissions; the emissions of a cold machine would simply "taste" different from those of a fellow Vulcan or a Klingon or a Horta.
Better yet, how did she get her personal memories back?
I'll raise by asking how any of her memories could ever have been removed. If memories are stored as basically chemical/physical connections within the brain, then removing them would mean removing her brain and killing her.
It sounds far more likely that Nomad did what computers do when they "erase" memory: it messed with some key connections related to the process of recollection, after which the brain would have been free to "overwrite" on the existing "memory slots" and treat them as "empty". None of the original connections would have been lost, though, so the process of re-education would be one of prying open the blockages created by Nomad. How McCoy managed to stop Uhura from "overwriting", we don't know - but it does seem that somehow the process of again learning to say "see Sally run" reopened the old memory reserves for regular recollection.