SQL Server : alternatives to INTERSECT - sql-server

Question

I am writing an attempt at implementing a name search functionality via a SQL Server stored procedure.
Three tables are involved with the following definitions:
Employee table (other columns removed for brevity)
CREATE TABLE Payroll.Employee
(
EmployeeID INT NOT NULL IDENTITY(1,1),
EmployeeName NVARCHAR(50) NOT NULL ,
CONSTRAINT PK_Employee PRIMARY KEY CLUSTERED (EmployeeID),
);
Names table (single names stored with a a unique KeyNameID)
CREATE TABLE Payroll.KeyName
(
KeyNameID INT NOT NULL IDENTITY(1,1),
KeyName NVARCHAR(20) NOT NULL ,
RwVersion ROWVERSION NOT NULL
CONSTRAINT PK_KeyName PRIMARY KEY CLUSTERED (KeyNameID),
CONSTRAINT UC_KeyName UNIQUE (KeyName)
);
EmployeeName (employee's name stored using the id for each single name)
CREATE TABLE Payroll.EmployeeName
(
EmployeeNameID INT NOT NULL IDENTITY(1,1),
KeyNameID INT NOT NULL,
EmployeeID INT NOT NULL,
CONSTRAINT PK_EmployeeName PRIMARY KEY CLUSTERED (EmployeeNameID),
CONSTRAINT UC_EmployeeName UNIQUE (KeyNameID,EmployeeID)
);
The Employee table has the following rows:
INSERT INTO Employee (EmployeeID, EmployeeName) VALUES (1, 'ayub kassim');
INSERT INTO Employee (EmployeeID, EmployeeName) VALUES (2, 'eric yuda');
INSERT INTO Employee (EmployeeID, EmployeeName) VALUES (3, 'james kassim');
Each of the above names are split and stored in the KeyName table as follows:
INSERT INTO KeyName (KeyNameID, KeyName) VALUES (1, 'ayub');
INSERT INTO KeyName (KeyNameID, KeyName) VALUES (2, 'eric');
INSERT INTO KeyName (KeyNameID, KeyName) VALUES (3, 'james');
INSERT INTO KeyName (KeyNameID, KeyName) VALUES (4, 'kassim');
INSERT INTO KeyName (KeyNameID, KeyName) VALUES (5, 'yuda');
The KeyNameIDs are then used to identify each employee's single name as follows (two records per employee):
INSERT INTO EmployeeName (EmployeeNameID, KeyNameID, EmployeeID) VALUES (1, 1, 1);
INSERT INTO EmployeeName (EmployeeNameID, KeyNameID, EmployeeID) VALUES (2, 4, 1);
INSERT INTO EmployeeName (EmployeeNameID, KeyNameID, EmployeeID) VALUES (3, 2, 2);
INSERT INTO EmployeeName (EmployeeNameID, KeyNameID, EmployeeID) VALUES (4, 5, 2);
INSERT INTO EmployeeName (EmployeeNameID, KeyNameID, EmployeeID) VALUES (3, 3, 3);
INSERT INTO EmployeeName (EmployeeNameID, KeyNameID, EmployeeID) VALUES (3, 4, 3);
My search code is as follows:
CREATE PROCEDURE dbo.uspEmployeeSearch
#SearchString1 NVARCHAR(20),
#SearchString2 NVARCHAR(20)
AS
DECLARE #StringLength INT = LEN(#SearchString2)
SELECT #SearchString1 = RTRIM(#SearchString1) + '%'
SELECT #SearchString2 = RTRIM(#SearchString2) + '%'
SET NOCOUNT ON
IF #StringLength = 0
SELECT
EmployeeName,
taxpin
FROM
Employee
JOIN
EmployeeName ON Employee.EmployeeId = EmployeeName.EmployeeId
JOIN
KeyName ON KeyName.KeyNameId = EmployeeName.KeyNameId
WHERE
KeyName.KeyName LIKE #SearchString1;
ELSE
SELECT
EmployeeName,
taxpin
FROM
Employee
JOIN
EmployeeName ON Employee.EmployeeId = EmployeeName.EmployeeId
JOIN
KeyName ON KeyName.KeyNameId = EmployeeName.KeyNameId
WHERE
KeyName.KeyName LIKE #SearchString1
INTERSECT
SELECT
EmployeeName,
taxpin
FROM
Employee
JOIN
EmployeeName ON Employee.EmployeeId = EmployeeName.EmployeeId
JOIN
KeyName ON KeyName.KeyNameId = EmployeeName.KeyNameId
WHERE
KeyName.KeyName LIKE #SearchString2
The procedure expects two parameters. Where only one name is being searched, the second parameter would be a zero-length string.
So far it works with around 31% of the cost on SORT. The nested loops use 'index seek' which is good for me.
In short, if I am searching for 'ayub kassim' I only want employee records with the full name 'ayub kassim'. But if I search for 'kassim' I want all employee records with 'kassim' in the name.
My question is: Is it possible to implement this stored procedure using JOINS only, without the proprietary INTERSECT clause?
For the record I do not want to use LIKE because I need a very fast procedure and my employee table could run into hundreds of thousands of records.
Thanks in advance for your help.