Keep the original first and surnames in the table, do not overwrite them, in case you ever need to get back to the base source data (imho) it is easier to re-merge them than to split them apart :)
ALTERNATIVELY - do not merge at all (I hate making clean data dirty), and change your select to:
SELECT [Name_First] + ' ' + [Name_Last] as [Name_Full] from [list] where <whatever> order by <whatever>