SQL Server 2019

By using db<>fiddle, you agree to license everything you submit by Creative Commons CC0.
create or alter function dbo.foo()
returns table 
--with schemabinding
-- Msg 2720 Level 16 State 1 Line 6
-- Cannot schema bind table valued function 'dbo.foo' because it references system object 'sys.objects'.
as
return (
       select 
          x = OBJECT_SCHEMA_NAME(@@PROCID) 
          ,y =OBJECT_NAME(@@PROCID)
          ,z =(select top 1 object_id from sys.objects where object_id=@@PROCID)
);
select * from dbo.foo();


x
y
z


null
null
null


create or alter proc dbo.bar
as
begin
   select 
        x= OBJECT_SCHEMA_NAME(@@PROCID)
        , y = OBJECT_NAME(@@PROCID)
        ,z =(select top 1 object_id from sys.objects where object_id=@@PROCID)
end;
exec dbo.bar;


x
y
z


dbo
bar
597577167


create or alter function dbo.baz()
returns varchar(100)
as
begin
    declare @i int = (select top 1 object_id from sys.objects where object_id=@@PROCID);
    return isnull(convert(varchar(10),@i),'NULL') + '-' + isnull(OBJECT_SCHEMA_NAME(@@PROCID),'NULL') + '.' + isnull(OBJECT_NAME(@@PROCID),'NULL');
end;
select dbo.baz()


(No column name)


NULL-NULL.NULL


SELECT OBJECT_NAME([object_id]), object_name(object_id), is_inlineable --, definition
  FROM sys.sql_modules
  where object_name(object_id) in ('foo','bar','baz');


(No column name)
(No column name)
is_inlineable


foo
foo
True

bar
bar
False

baz
baz
True