Count based on condition in SQL Server

I think he wanted user id in the results

SELECT 
    userid,
    COUNT(*) as TotalcaseID, --total 
    SUM(CASE WHEN name = 'system' THEN 1 ELSE 0 END) as TotalRecordsWithSystem  
FROM 
    myTable 
group by userid

Use SUM/CASE...

SELECT
    COUNT(*),  --total
    SUM(CASE WHEN name = 'system' THEN 1 ELSE 0 END) --conditional
FROM
    myTable