Really interesting start with the short story. It definitely hit all the beats of "awakening AI intelligence" - I think it would have been awesome to take the ball even further and get into the character's motivations a bit deeper.
For example: why does P35 / Porter want a name without numbers? What makes them want to be more like the scientists/lab folk instead of deciding - for example - think they are special for having such a unique name? As a being that interprets the world through numbers, why not prefer a system of binary on/offs for a name? Etc