Oracle doesn't permit the creation of index with the same name in the same schema. Are your indexes in seperate schemas? if Yes, then please specify your schema.index_name while deletion.To check the schemas of index , you can query all_indexes.
select * from all_indexes where index_name = 'put your index name here';
Then you can log in to one of the schemas and run delete schema_name.index_name. It must be a privilege issue hence you are getting an error