your plant is a Drimiopsis maculata. It's indigenous to south eastern South Africa. It is evergreen and makes a great shade plant - I use it as ground cover / filler plant under shrubs. :-)
The only thing it has in common with Eucomis is that they are in the same family - Hyacinthaceae. (Eucomis always has leaves at the top end of the flower stalk, and they are a LOT bigger)
I have this very same plant, Evert, and it looks just like yours! Four or five leaves and one slender bloom stalk even. I was told it was African Hosta, but didn't know the botanical name. I looked at pics of Maddy's suggestion, Drimiopsis maculata, and I do think that's just what it is.
Thank you so much my friend in the same time zone and Linda :) I think it is that. I have to repot mine... nice to know it is something rarer, I like rare species. (OR at least it is pretty rare here ;))