I'm not sure about the name pronounced Neta meaning seedling although it does sound like a more recent convention.
There is a similar name Nota (נטע ) for ashkenazi men that often accompanies the name Nosson or Nathan. I think it is more of a nickname for נתן and isn't really connected to planting despite the spelling.
The author of the kabbalistic work מגלה עמוקות was Rabbi Nosson Nota Shapiro of Krakow born 1584, and the name was used even earlier than that.
Hope this helps.