I am not interested in the contents of a row, I just want to know if a row exists. The Name column is a primary key, so there will either be 0 or 1 matching row
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;