I'm using generalized linear models and generalized nonlinear models in a modeling project, so I refer to the final predictor simply as the predictor. But I find that this is confusing and unclear, as you can also refer to the predictor variables as predictors. Is there another way to refer to the final predictor, or any other way to distinguish the final predictor and predictor variables?
I think it's a bit odd to talk about the "final predictor". Usually, one talks about the "final model" and then elaborates on what predictors were included in that model (relative to the "initial model").
You may find the post available at https://www.theanalysisfactor.com/whats-in-a-name-moderation-and-interaction-independent-and-predictor-variables/ interesting. The post talks about the terminology "predictor variable" and mentions that there are many subtypes of predictor variables.
If your models are used for prediction, then the terminology "predictor variable" certainly makes sense. If they are used for explanation (i.e., to uncover and quantify associations), perhaps you could use the terminology "explanatory variable" instead of "predictor variable". If they are used for both explanation and prediction, you could revert back to the "predictor variable" terminology.
In any event, if you make it clear what predictor/explanatory variables you started out with in your "initial model" and what predictor/explanatory variables you were left with in your "final model", there should be no confusion.