Separate An And/Or Parameter

I want a user to be able to search for names in a table of clients
using a single parameter, but be eable to use "and" or "or" IN the
parameter.
Like this:

@NameSearch nvarchar(100)

AS

DECLARE @PartA nvarchar(100), @PartB nvarchar(100)

CASE When @nameSearch Like '%' + ' OR ' + '%'

SELECT @PartA =(how do I get what's to the left of "OR" or "AND")
SELECT @PartB (how do I get what's to the right of "OR" or "AND")

SELECT
c.UniqueID,
c.LastName
FROM
dbo.tblClients c
WHERE
c.LastName = @PartA
OR
c.LastName = @PartB

CASE ELSE

SELECT
c.UniqueID,
c.LastName
FROM
dbo.tblClients c
WHERE
c.LastName = @NameSearch