What do you call cider and blackcurrant cordial?

There isn't a widely recognized name for a mix of cider and blackcurrant cordial. It's simply referred to as cider with blackcurrant cordial.

You could also use descriptive terms like:

* Blackcurrant cider

* Cider with blackcurrant

* Blackcurrant-infused cider

Ultimately, the best name depends on how you want to present it!