The product is super cool and useful, although I hope you won't limit it to being a single-user thing because it could actually evolve into an amazing social tool. But I would really lose the word 'manage', it kind of suggests that personal relations are just another kind of task which is apt to make the people being related to feel devalued because they're not important enough to be given space in someone's day-to-day consciousness.

poetic terms that say nothing

?!

If poetic terms say nothing then why is poetry (both literary and lyrical, as in songs) so popular? Social relations are not purely functional or transactional, although they often have those aims or characteristics. Friendship and warm familial relations are based on feelings. I often say that hackers need to develop better emotional intelligence and this is a good example.

Would you take someone on a date and say 'statistics indicate that we have a high degree of socioeconomic compatibility and synergistic aesthetic appeal, suggesting that we should pursue a merger strategy so as to maximize our mutual future advantage?' Most people would prefer to hear something along the lines of 'I love you and want to marry you.'

I understand that your product is aimed at busy people who are invested in their work and want to handle their social relations at least as well as their business ones. But you need to be cognizant of their motivations for doing that; because they like, love and generally care about the people in their lives that lie outside their career. It is that drive which might move someone to start using your product, and you must appeal to that drive, which is an emotional one, in emotional terms.

Incidentally, calling it Monica carries connotations of having an assistant called Monica that helps you remember those little personal obligations and although I'm sure you didn't intend this it gives me a sort of sexist vibe because historically such tasks have often been delegated to stereotypically female subordinates by busy executives (think Pepper Potts in the Iron Man story franchise).

Even though both men and women seem to prefer female identities for things like GPS and virtual assistants, a gendered brand identity like this is likely to limit your appeal to one half of the population straight out of the gate. The brand values you wish to attach to your product are reliability, loyalty, and patience, so it would be worth your while to dig through mythology and fiction in search of characters who are associated with those qualities and then develop variations from any particularly inspiring name stems you encounter so as to leverage those psychic associations.