"wife: Arthur" - yeah, this will be well received by modern audiences.
So you'd engage in social interactions so that they liked you, and felt you brought them prestige and power. Attend their Social Occasions, probably do some intermarriage, spend personal time with them focusing on their Interests, occasionally fulfill their top desires.
To what an extent can the player actually have a presence in the in-game world? Lets say I'm attending a Social Occasion. In CK2/3 I'd probably get a text notification - "[Character] has arrived at a feast here and there" and then "+15 relation with the organiser" + maybe some kind of little story events in a CYOA formula. Should I expect the same from Axioms?
Well technically her name is Artur
Also plenty of unisex names in modern times, like Ashley. In any case those are randomly generated names only with some rules about adding extra vowels. On release there will be proper name generating system.
So Social Occasions have a few different aspects. First whether you accept the Invitation and if you didn't why, maybe you had a previous engagement for maybe you want to insult the host or w/e. Once you accept an Invitation and show up there are a few things that will happen. Obviously the Host has more options than a guest but you still have a few things to do depending on the type of event.
So as the Host you send out Invitations that are individually decided regarding the activities the guest is invited to, special directions like sitting at the high table for a feast, and who they can bring with them. Spouse, kids, a friend, etc. At each "Activity" there is a general bonus based on your event preparation modified by the "Interests", Personality, and "Desires" of each guest, and then you have the option to take some number of Social Occasion Actions. Some is just like give a toast to a Character, Population, or Organization. They'll like you more, and there can be other effects as well based on specifics. You can give other people the chance to make a Toast as well. You have some total number of Actions you can take and you can pick what you do with them. You can chat up a guest, give a gift, and some other stuff.
As a Guest you have a number of Actions you can take as well. You can also chat with other guests, in some cases picking a special location or part of the venue, you can choose which events to go to based on what you were invited to, do small group socializing, and like for the Host other guests may try to interact with you themselves. At a dance/ball you'd choose people to dance with, and if you were trying to "court" someone you might mostly dance with them, assuming they enjoy dancing or take them to a romantic part of the venue or w/e.
For the player, there's a full Menu/set of panels that you interact with to do all this stuff, and not just a couple pop ups like in CK2/CK3. There's only random events in so far as other Characters choose to try to interact with you. And every Character is taking at least a few Actions.
The Host has a bunch of decisions to make as far as organizing events, which is not a thing in Paradox games. I guess Royal Court is vaguely similar in a very simplistic way with the decorations and stuff to get Grandeur? Axioms has a resource economy with Resources, Products, Items, and Buildings and stuff, sort of like a city builder with RPG/MMO crafting but not a physical city map. Buildings are stored on the Province level without "positions". So you have to actually have the food, gifts, decorations, buildings, creatures, staff, and charactes involved in holding an event. And after the food is eaten it is taken out of your storage. Entertainment like Music or Dancers, or Carnival stuff exists in the world as well. Well I think Carnivals might be part of the first expansion. There's a lot of work so they can travel around and do stuff. A "Magic Show" or a "Bardic Performance" can be performed by Characters with those skills. Not every Character would have access to that for their events. Tournaments and Duels are somewhat more detailed as well. Bets, seating, picking a favorite so you get bonuses if they do better, and so forth, and again all attendees would do this. Religious Rites would be specific to each religion, and a sacrifice would require your to actually have "super awesome cows" or w/e. It isn't just a gold cost like in Paradox games. And of course if you read my blog you know that Social Occasions are one place where, knowing certain people will be in certain locations, you can perform various intrigue related Actions. Ambushing carriages on the road, poisoning, blackmail, various spell based Intrigue, and so forth.