If there is no rule “Memories”, create it.
Reword the rule “Memories” to the following:
There is a publicly tracked list of Memories, defaulting to blank. Each Memory has a publicly tracked ID which can be any Integer not already held by a Memory, and a publicly tracked Owner, which can be any Innie or blank (default), a publicly tracked flavor text Fragment, which may be a text string or blank (default), and a publicly tracked flavor text Context, which is a statement about that Memory’s Owner that can be true or false in the current gamestate and which is, by default, “This Memory’s Owner is an Innie”. An Innie’s Memory is Active when its Context is true and Suppressed when its Context is not true.
As a Weekly Action, an Innie may Train Memory. When an Innie Trains Memory, he creates a new memory with him as the Owner, and randomly chooses a context from the below list, and applies any instructions in brackets associated with that
Context:
*This Memory’s Owner Owns a X (then roll {Finger Trap, Specialized Algorithms} and replace X with the result)
*This Memory’s Owner Has a Stress of X (then roll a DICE5 and subtract 1, replacing X with the adjusted result)
*This Memory’s Owner Has a Reprimands of X (then roll a DICE7 and subtract 1, replacing X with the adjusted result)
*This Memory’s Owner’s Department has a Quota of 0
*This Memory’s Owner has posted a Report and there is no Voting Icons in the Board’s Comments on it.As a Daily Action, any Innie or the Board may change the Context of any Active Memory to “This Memory’s Owner is a Innie.”
As a Daily Action the Board may choose the Active Memory with a Fragment of Blank, and the Smallest ID, and then the Board randomly chooses a line from this list and follow the instructions.:
*Use the random name generator at https://www.behindthename.com/random/ to randomly select a name (the Board may change the settings on the Random Name Generator before doing so), and then set the selected Memory’s Fragment to “Your Name is N”, where N is the generated name.
This fleshes out Memories so you can play the minigame (though it has no effect yet). Basically, you try to activate a trigger and once that trigger is completed, you remember something.

SingularByte: he/him
If I’m reading this correctly, you can end up with multiple names if you have multiple memories picked by the Board? Also I’m not quite sure what the point of the harder contexts are when you can just swap it immediately to always be Active.