the only way that it seems to me is to pass the procedure name explicitly through CONTEXT_INFO it goes into the procedure
declare @bin varbinary(128) = (cast(object_name(@@Procid) as varbinary(128)) set context_info @bin
and use it in a trigger
declare @procName as nvarchar(max) set @procName = cast(context_info() as nvarchar(max))
I do not know another way to do this.
edit: I think you might be interested clickie
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