Take a minute to think about who your users are. In what cases are they more likely to re-type the same name by accident? In these cases, are they more likely to want a very similar name to be applied automatically (I doubt you can find a transformation method that applies to any field names in elegant ways..), to delete or merge the now duplicate item they were renaming, to give it a different name of their own, or to revert back to the previous step (a case which I have trouble finding a rationale for, other than findability: at least it's easy to figure out what transformation occurred).
Try and decide what are the high probability desirable outcomes, and then think in those terms: at the moment the user is done typing or editing, what feedback/action provides the cheapest interaction cost for reaching the user's most desirable outcomes?
For instance, let's assume my users sometimes want a) to merge the two identically-named fields, b) to type an entirely new name and c) to revert to the previous name. They have a keyboard in this setup.
I would go back to the field in edit mode, select all the field's name so users can delete it in one keyboard stroke and type a new one right away. I would provide the abilities to merge and revert to the previous name with specific links displayed on a popover (think GMail's "undo" popover when deleting emails, http://www.svennerberg.com/2008/07/no-undo-redo/). Besides clicking away or pressing Esc after the name conflict has been highlighted should revert to the previous option.
A second example: now my user is on a touch-oriented device, typing is painful and field names are made of several long words. Add whatever condition makes you think that users may create multiple fields with similar wording. Now the desirable outcome would be to keep what was typed so far and just modifying it oneself. It'd be disastrous to just remove everything the user typed. KMSTR's suggestion is probably the best you can do.
Generally speaking, it's almost always a bad idea to do something different from what the user expected without telling them. They might notice only much later after they had started doing other things assuming you respected their original intent (see the concept of interaction breakdown for more on that).