How to rename index of column in Entity Framework?

I'm using .NET 4.7 with EF 6.2 and I want to rename the name and the index of one of my columns.

I have a table Students and first:

  1. I'm renaming one of the columns Name to FirstName in my migration file I'm using

    RenameColumn("dbo.Students", "Name", "FirstName");
    

    Later translated to SQL it is

    EXECUTE sp_rename @objname = N'dbo.Students.Name', @newname = FirstName', @objtype = N'COLUMN'
    

    and there is no problem the column is renamed.

  2. Then instead of dropping the index and creating it again I'm trying just to rename it with

    RenameIndex("dbo.Students", "Name", "FirstName");
    

    In SQL Server it is like

    EXECUTE sp_rename @objname = N'dbo.Students.Name',@newname = FirstName', @objtype = N'INDEX'
    

    Then just for as a test, I manually run that SQL script in SQL Server Management Studio (SSMS) and it throws an exception:

    Either the parameter @objname is ambiguous or the claimed @objtype (INDEX) is wrong

For that exception I have reаd some of the other questions here, but it doesn't helped me.

Then I tried to reverse the steps first to rename the index and then to rename the column, but the result was the same.

Why does that exception occur, and how to rename index of a column using EF?