Try this one
DECLARE @Table TABLE(Name varchar(100))
insert into @Table values('Nikhil Nikhil')
insert into @Table values('Nikhil Ram')
;with cte as (
select *,SUBSTRING(Name,0,CHARINDEX(' ',Name)) FirstName,SUBSTRING(Name,CHARINDEX(' ',Name)+1,LEN(Name)-CHARINDEX(' ',Name))LastName from @Table
)select Name Original_Name,case when FirstName=LastName then FirstName Else Name End New_Name from cte