In ADO.NET, correctly handling null is a constant source of confusion. The key point in dapper is that you don't have to; it deals with it all internally.
null are correctly sent as DBNull.Valuenull are presented as null, or (in the case of mapping to a known type) simply ignored (leaving their type-based default)It just works:
string name = null;
int id = 123;
connection.Execute("update Customer set Name=@name where Id=@id",
new {id, name});