You can do it by first unlinking the plant from the database, then changing the name and saving the change, then linking it to the database again. A little cumbersome, but it seemed to work when I tried it.
Fnd the plant in your plant list and click the 2nd icon from the top on the left-hand side of the page (it looks like a striped cylinder). Choose "unlink this plant from the database."
Return to your "lists management area" and find the plant - it should be near the top of your list. Click the top icon on the left-hand side of the page to edit your entry and change it to whatever you want. Save your changes, then go back to the plant and click on the 2nd icon again, select the plant name from the database that it matches, and choose to link the plant to the database. Now it should be back in your list in the appropriate place, with all of the info that you had originally entered.