Disclaimer: I know nothing (well, very little) about Macs. The only suggestion I can make to fix the problem is to delete the preferences file. To do this, hold down the Option+Command+Shift keys immediately after launching the Organizer. You will be presented with a dialog asking if you want to delete the Settings file. Answer Yes. (If you don't see the dialog, try holding down the keys before launching the Organizer.) If you need more assistance with this, see this Help article.
When you type in the whole name, aren't you seeing a dialog that says something like That name already exists with some options? In any event, you can select the duplicate People stacks, right-click on them, and you will then have a context menu that allows you to merge the stacks. (At least, that's what happens in Windows. I expect it is similar on a Mac.)
Added: When you select the duplicate stacks, the Rename button at the bottom of the screen changes to Merge People: