It's virtually the same process as when looking up this data from a different table.
Go to Manage | database | Relationships.
Make a copy of the Tutorial: What are Table Occurrences? box that represents your table and which is the table occurrenc on which your layout is based. Then define a relationship that links the two occurrences of the same table by your name field. (but an ID field is better. You can get two people in your table with identical names or a person might change their name....)
Then you set up the same auto-enter field options to copy data from the related record as you would if this added table occurrence represented a different table altogether.
(Note, unless you set up the relationship differently, this will always fill in data from the oldest matching record. There are ways to set up a sort order for the relationship that would copy over data from the most recently added matching record.)