Did you copy names too into new table? Because the simpliest would be to add an empty FirstName field to your old table, rename the Name field as LastName, and then to run an update query to fill the Firstname column with initials form LastName, and to replace entries in LastName field with last names without initial an dot from same column.
Something like (on fly, and it assumes you have always a space after dot, otherwise you have to search for lastname also the dot, and then Trim() the whole expression)
Code:
UPDATE YourTable (FirstName, Lastname)
SET Firstname = Iif(InStr(".",LastName)>0,Left(LastName,InStr(".",LastName)),Null), LastName = Iif(InStr(".",LastName)>0,Right(LastName,Len(LastName) - InStr(" ",LastName)),LastName)