Out of duty i went to see the Genisys as well. Lukewarm rehash at best, not worth the popcorns. Save your money for something better. Although big Arnie had one catchy line in addition to the “i’ll be back” and that was “old but not obsolete”. I shared the feeling :D.
About names. The list Jim linked is practically definitive so there is not much to add to that. One thought comes to mind however, since the bot is not really a physical robot as such, more an actor behind the curtains so to speak. If anyone is into scifi and has read Willian Gibson’s “Neuromancer” - the book that launched cyberpunk as a genre and presaged the Internet and was generally a mind blower (https://en.wikipedia.org/wiki/Neuromancer), you might remember Wintermute. The shadowy AI scheming and guiding destinies without anyone getting the wiser. Could be big shoes to step into but why not - let that be my 2 c worth of suggestion.
P.S. for those who might be interested, the full text of Neuromancer: https://7chan.org/pr/src/A_neuromancer.pdf