How i can prevent from repeating 'unit_name' in table

You can modify the stored procedure to validate the existance of the unit_name before inserting as below. Below code is not tested.

ALTER proc [dbo].[unit_ins](@vv unit_insert readonly)
as
begin
        if not exists(select null from unit where  unit_name in (select unit_name from @vv))
        insert into unit(unit_name)
end

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Regards, RSingh