T-SQL speed comparison between LEFT() vs. LIKE operator
Your best bet would be to measure the performance on real production data rather than trying to guess (or ask us). That's because performance can sometimes depend on the data you're processing, although in this case it seems unlikely (but I don't know that, hence why you should check).
If this is a query you will be doing a lot, you should consider another (indexed) column which contains the lowercased first letter of name and have it set by an insert/update trigger.
This will, at the cost of a minimal storage increase, make this query blindingly fast:
select * from table where name_first_char_lower = @firstletter
That's because most database are read far more often than written, and this will amortise the cost of the calculation (done only for writes) across all reads.
It introduces redundant data but it's okay to do that for performance as long as you understand (and mitigate, as in this suggestion) the consequences and need the extra performance.
"Left" vs "Like" -- one should always use "Like" when possible where indexes are implemented because "Like" is not a function and therefore can utilize any indexes you may have on the data.
"Left", on the other hand, is function, and therefore cannot make use of indexes. This web page describes the usage differences with some examples. What this means is SQL server has to evaluate the function for every record that's returned.
"Substring" and other similar functions are also culprits.
I had a similar question, and ran tests on both. Here is my code.
where (VOUCHER like 'PCNSF%'
or voucher like 'PCLTF%'
or VOUCHER like 'PCACH%'
or VOUCHER like 'PCWP%'
or voucher like 'PCINT%')
Returned 1434 rows in 1 min 51 seconds.
vs
where (LEFT(VOUCHER,5) = 'PCNSF'
or LEFT(VOUCHER,5)='PCLTF'
or LEFT(VOUCHER,5) = 'PCACH'
or LEFT(VOUCHER,4)='PCWP'
or LEFT (VOUCHER,5) ='PCINT')
Returned 1434 rows in 1 min 27 seconds
My data is faster with the left 5. As an aside my overall query does hit some indexes.