SQL Update Stored Procedure involving Subqueries

I have a few table's in my DB.

I am trying to update the rota table using a SQL stored procedure. I want the user to be able to type in, for example;

Name: Adam Brookes

Shift: Middle Day

On Call: Secondary

and using a subquery have it look up the id's of those and place them into the rota table. At the moment I am testing in Postman where I can define the 'date' and 'datekey' manually.

My Stored Procedure currently looks like this;

ALTER PROCEDURE [dbo].[RotaUpdateItems]
    @date_key int,
    @date date,
    @user_id varchar(max),
    @shift_type_id int,
    @type_call_id int

AS
BEGIN

    SET NOCOUNT ON;

    UPDATE rota
    SET date = @date,
        user_id = (
        SELECT user_id 
        FROM staff s
        WHERE s.first_name LIKE 'ABC%'
        ),
        shift_type_id = (
        SELECT shift_type_id 
        FROM shifts h
        WHERE h.shift_type LIKE 'ABC%'
        ),
        type_call_id = (
        SELECT type_call_id 
        FROM on_call c 
        WHERE c.type_of_call LIKE 'ABC%')
    WHERE date_key = @date_key
END

I have referenced this question to get the LIKE 'ABC%' code to see if that would help convert "Primary" into '1', but this did not fully answer my question

I also researched this answer from John to see if a join is necessary when running an update query but this did not fully answer my question.