What you need is a split user-defined function. With that, the solution looks like
With SplitValues As
    (
    Select T.Name, Z.Position, Z.Value
        , Row_Number() Over ( Partition By T.Name Order By Z.Position ) As Num
    From Table As T
        Cross Apply dbo.udf_Split( T.Name, ' ' ) As Z
    )
Select Name
    , FirstName.Value
    , Case When ThirdName Is Null Then SecondName Else ThirdName End As LastName
From SplitValues As FirstName
    Left Join SplitValues As SecondName
        On S2.Name = S1.Name
            And S2.Num = 2
    Left Join SplitValues As ThirdName
        On S2.Name = S1.Name
            And S2.Num = 3
Where FirstName.Num = 1
Here's a sample split function:
Create Function [dbo].[udf_Split]
(   
    @DelimitedList nvarchar(max)
    , @Delimiter nvarchar(2) = ','
)
RETURNS TABLE 
AS
RETURN 
    (
    With CorrectedList As
        (
        Select Case When Left(@DelimitedList, Len(@Delimiter)) <> @Delimiter Then @Delimiter Else '' End
            + @DelimitedList
            + Case When Right(@DelimitedList, Len(@Delimiter)) <> @Delimiter Then @Delimiter Else '' End
            As List
            , Len(@Delimiter) As DelimiterLen
        )
        , Numbers As 
        (
        Select TOP( Coalesce(DataLength(@DelimitedList)/2,0) ) Row_Number() Over ( Order By c1.object_id ) As Value
        From sys.columns As c1
            Cross Join sys.columns As c2
        )
    Select CharIndex(@Delimiter, CL.list, N.Value) + CL.DelimiterLen As Position
        , Substring (
                    CL.List
                    , CharIndex(@Delimiter, CL.list, N.Value) + CL.DelimiterLen     
                    , CharIndex(@Delimiter, CL.list, N.Value + 1)                           
                        - ( CharIndex(@Delimiter, CL.list, N.Value) + CL.DelimiterLen ) 
                    ) As Value
    From CorrectedList As CL
        Cross Join Numbers As N
    Where N.Value <= DataLength(CL.List) / 2
        And Substring(CL.List, N.Value, CL.DelimiterLen) = @Delimiter
    )