use master
alter database [MY_DATABASE]
add filegroup [B]


alter database [MY_DATABASE]
 add file
    (
    NAME        = N'new_logical_name01',
    FILENAME    = N'X:final_name.mdf',
    SIZE        = 100GB,
    FILEGROWTH  = 1500MB
    )
    to filegroup [B]

set nocount on
declare
    @sql nvarchar(max) = '',    --dynamic sql
    @name varchar(100) = '',    --name of table
    @schema varchar(100) = '',  --name of schema
    @c1 sysname = ''            --name of first column

declare test cursor for
    select distinct
        object_name(i.[object_id]) as name,
        s.name as s
    from       sys.filegroups   as f
        inner join sys.indexes      as i    on f.data_space_id = i.data_space_id
        inner join sys.all_objects  as a    on i.object_id     = a.object_id
        inner join sys.tables       as t    on a.object_id     = t.object_id
        inner join sys.schemas      as s    on t.schema_id     = s.schema_id
    where 1=1
    and a.type ='U'         -- object type
    and f.name in ('A')     -- name of old filegroup

open test
fetch next from test into @name, @schema
    while (@@FETCH_STATUS <> -1)
    begin
       set @sql = 'if exists (select * from sys.indexes where name = ''idx1_mover'' and object_id = object_id(''' + @name + ''')) drop index [' + @name + '].idx1_mover'
exec sp_executesql @sql
set @c1 = (select top 1 a.name from sys.columns a inner join sys.tables b on a.object_id = b.object_id and b.name = @name order by a.object_id)
set @sql = 'create clustered index idx1_mover ON [' + @schema + '].[' + @name + '] ([' + @c1 + '])
    with (data_compression = page)
    on [B]' --name of new filegroup
    exec sp_executesql @sql
    set @sql = 'drop index [' + @schema + '].[' + @name + '].idx1_mover'
    exec sp_executesql @sql
    fetch next from test into @name, @schema
end
close test
deallocate test

dbcc shrinkfile (N'old_logical_name01' , EMPTYFILE) --logical filename of files in filegroup A
dbcc shrinkfile (N'old_logical_name02' , EMPTYFILE)
dbcc shrinkfile (N'old_logical_name03' , EMPTYFILE)
--...

alter database [MY_DATABASE] remove file [old_logical_name01]
alter database [MY_DATABASE] remove file [old_logical_name02]
alter database [MY_DATABASE] remove file [old_logical_name03]
--...

alter database [MY_DATABASE] remove filegroup [a]

alter database [MY_DATABASE] modify filegroup B name=A

alter database [MY_DATABASE]
modify file
    (
    NAME    = N'new_logical_name01',
    NEWNAME = N'old_logical_name01'
    )
--...