How do I get a linked list to display more then just the first search item in Access?
One option would be to create a display column fullName that concats your first and last name values into a single column. I believe the following should work in your Row Source:

SELECT [Table1].[ID], [Table1].[lastName] &amp; ", " &amp; [Table1].[firstName] as fullName, [Table1].[Position]
FROM Applicants
ORDER BY [Table1].[lastName] &amp; ", " &amp; [Table1].[firstName];


A couple notes:

Even though we alias [Table1].[lastName] &amp; ", " &amp; [Table1].[firstName] as fullName, we can't order by the alias, so we repeat the expression in the ORDER BY.

Using the above query, your column count will be 3 instead of 4, so you may need to change the column count property of the ComboBox. 

I'm not very Access savvy, so I'd suggest checking other properties to make sure I haven't missed anything else.