Ledger vs ledger set

Hello All,

We have to define one Primary ledger , and then oracle will create a ledger set with same name having primary ledger and its reporting ledger.

By mistake , with out defining primary ledger we created ledger set with same name.

Now oracle not allowing us to create primary ledger with same name  to delete the ledger set defined .

We want to create the primary ledger with the same name and short name as we follow the naming conventions  which we cant deviate.

Is there any way that we can define primary ledger with same name ?

Thanks,

Raj