This is how the error message looks now:
123 Msg 2628, Level 16, State 6, Procedure ProcedureName, Line LinenumberString or binary data would be truncated in table ‘%.*ls’, column ‘%.*ls’.Truncated value: ‘%.*ls’.Notice how the table, column and value are all mentioned in the error message now, which makes debugging and troubleshooting much easier. Thank you Microsoft!
As of 24 October 2018, we can now get the full picture in SQL Server 2017 as well, provided we install Cumulative Update 12. I’d say this is worth the update in and of itself!
There is a trace flag involved, so check it out.