The best way may be to remove the doctor name look up field from your database as unneeded. Just add the doctor name field from your new table to the layout for your original table. If you have a doctor ID selected in each of your existing records the relationship linking your two tables by ID will enable FileMaker to put the correct doctor name in that field.
But if you insist on keeping that lookup field, if it uses the looked up value auto-enter field option, you can show all records, put the cursor in the id field and then use Relookup to relookup this name for all records in your found set.
If you used an auto-enter calculation, see this method: Updating values in auto-enter calc fields without using Replace Field Contents
But this all assumes that you've updated all your old records with ID's. You may want to temporarily add another Tutorial: What are Table Occurrences? of your new table and link it by Doctor name fields to your original table, then use Replace Field Contents to copy over Doctor ID's. Once this one time fix is complete, you can remove the added table occurrence.
is there a reason why you can't do this as a calculation rather than a lookup ? that way it will work for both new and existing records.
You still have to get the IDs in place first on your older records. And why use any field at all? Once you have linked by IDs, you can use the field from the new related table.
perfect many thanks .