What is the fastest way to determine if a row exists using Linq to SQL?

The Count() approach may do extra work, as (in TSQL) EXISTS or TOP 1 are often much quicker; the db can optimise “is there at least one row”. Personally, I would use the any/predicate overload:

if (dc.Users.Any(u => u.Name == name)) {...}

Of course, you can compare what each one does by watching the TSQL:

dc.Log = Console.Out;