I don't see how it would be "way better" to export this data to another table. Can you explain what advantages you see to using that method? It may be that we can suggest an alternative approach that does not require exporting your data like this and then you have a much simpler system to manage.
Does each "name" appear only once in the table you are searching?
Is there a primary key field that uniquely identifies each record?
If it really is necessary to use a temp table, it's entirely possible that all you need do is acquire a list of primary keys from your found set to export to your temp table and then a relationship can use them to access the data in your original table--keeping the duplication of dat to a minimum. This will require a bit of creativity to include the list of "missing" names, but this is possible with a bit of "sleight of hand" layout and data design.
Sorry, maybe I wasn't clear. I didn't mean it would be way better to use another table...it was actually my question if it would. With way better I meant that I wanted to get the same input list of names as output, also with missing names and in the same order.
Anyway, your suggestion to use the primary keys was very usefull and I used that method in a temp table to display the found data. Using a global field to store the not found names I made the missing names also appear in the list. So got it all working.