No, the leaves are too elongated to be nana. As to what they actually are I will leave to someone with more experience. Either way their basic needs are about the same.
Well I'll just throw these long leaf varieties out there for now. Not saying it is one of these but maybe you can research them and determine it yourself if no one else comes along to ID it. lanceolata, minima, rubescens, afzelii, afzelii angustifolia, barteri var. angustifolia just to get ya started