The place was overgrown with badri trees (Indian jujube).
To protect Vishnu, her husband, from the sun, Lakshmi turned herself into a badri tree.
In India, the husband is the ‚Lord‘ of the wife, so he is called Lord (Natha) of Badri, Badri in this case is Lakshmi.
Other names for Badrinath are Badrikakshetra and Badrikashrama.
Read about Badrinath here