LINQ: adding where clause only when a value is not null

you can write it like

IQueryable query = from staff in dataContext.Staffs;
query = from staff in query where (name1 != null && staff.name == name1);

This way second part of your condition will not be evaluated if your first condition evaluates to false

Update:
if you write

IQueryable query = from staff in dataContext.Staffs;
    query = from staff in query where (name1 == null || staff.name == name1);

and name1 is null second part of your condition will not be evaluated since or condition only requires one condition to return true

plz see this link for further detail