First, you need
1,10
in your SUBSTRING, not 0,10 - SQL indexes start at 1.
SELECT sobjects.name, st.row_count
FROM sysobjects sobjects
JOIN sys.dm_db_partition_stats st ON OBJECT_NAME(OBJECT_ID) = sobjects.name
WHERE sobjects.xtype = 'U' and SUBSTRING(sobjects.name,1,10) = 'MyFirstTenCharacter'