just a thought here...

Direct your Lookup Match Output to another Lookup - use the same setup as you did before ut this time look up and slecect both the id and name. Direct your Lookup No Match Output to an update...or another staging table and do a set-based update in an Execute SQL Task. I'll explain the differences below

If you don't mind row-by-row processing, map your non-matching output of the second lookup to an OLE DB Command and write and update to update the name based on the id. This will do in a pinch but will take a really long time if you have several records.

I suggest creating a staging table and directing the non-matching output of the second lookup to be inserted into it.

Then back in the control flow, after the data flow transfor use an execute sql task to perform a set-based update on your destination table from your staging table joining on id.

If you use the staging table method, be sure to put another Execute SQL task before your data flow task to truncate the staging table 🙂

Good luck!