Inference over a fixed term - what analysis am I doing here?

I have a fixed term of, say, one year. At the end of the term there is an observation of true / false, say a customer either renews or cancels their subscription. This decision is probably based on the occurrence of certain events, say how many times did they use the service?, and maybe even the specific timing within this term.

At the beginning of the term (say, day 1) I don't have any behavioral information, so I can just use covariates to predict the end state. At the end of the term, when I can't do any interventions, I can use the gathered data. But what about halfway through the term or more generally at any time t?

Is there a generic name for this analysis you could point me towards so I can understand how to best build this model? It has elements of survival (with Type I censoring), longitudinal, and time series analysis. I'm wondering if there's an existing, well-understood path I can follow instead of making my own. I have looked into clinical and bond/duration analysis but don't know those fields well enough to know if they have situations that are similar to this. Thanks!