You shouldn't have been able to create a field with a duplicate name. But the [Mood] field was added as a User Field by JRiver at some time, so I guess an update could have added a duplicate field after you had added your field. That would be bad. I just checked the [Mood] field, and then tried to add another one. MC automatically changed the name of the new field to [Mood (1)], as it should. So I don't really know how you ended up with two [Mood] fields.
Deleting a User Field is easy. Just go to "Options > Library & Folders >Manage Library Fields" and select the field in the list. If the Delete Button becomes active, it is a User Field and can be deleted. If the Delete Button doesn't become active, it isn't a User Field, and you can't delete it. See the yellow highlights in the attached image.
As the JRiver created field, and your field, are both User Fields, you should be able to delete both, so be careful in selecting which one to delete. I advise changing the Display name for one of the fields and then checking if that field is the one that contains data. See the green highlights in the attached image, which shows a field name for one of my User Fields of [Favourite TV], with a Display name of "FTV".
You don't want to delete the field that contains data, as you will lose all the data. So as Jim suggests, backup your Library before making changes. If you find that there is data in both fields, come back and ask for more help, if you need to.