Assumptions:
You have built the new table and defined the fields.
The Name field has a unique index on it.
The ID field is an autonumber field

Use a query like this to append the records to the table.

INSERT INTO NewTable(UniqueNameField)
SELECT DISTINCT NameField
FROM TheOldTable
WHERE NameField Is Not Null

If you are using the query grid, then build the query with just the fields
you want to transfer, set the query's Unique VALUES property to Yes and then
select Query: Append Query from the menu.  You'll be prompted for the name
of the table you want to add records to and an Append To: row will appear
for you to specify the destination fields.