Hello and thanks for the comment!!! You aren't missing anything, there is currently no save function. I'll probably add one later when I have more content.
There's also way to see exactly how much HP an enemy has left, though for all the encounters, there are different descriptions/dialog when the enemy falls below specific health thresholds. Have you been finding that the encounters are too difficult/tedious?
I'll look into what's up with the name bug you mentioned! Thanks for pointing it out.
And you can call me Ich! :)