My first recommendation is: Try to set a PK on your DB, that would be great. Talk to your DBA, DevTeam, etc. If that isn't possible try to set the column as "NOT ALLOW NULL" then you can set the PK at the LLBLGenPro Designer.
If nothing of above is possible, the only way (AFAIK) is this (_UpdateEntitiesDirectly_):
// (Assuming Adapter TemplateSet)
// given a fetched PersonEntity named thePerson
thePerson.Name = "name updated";
... other fields
IRelationPredicateBucket filter = new RelationPredicateBucket();
filter.PredicateExpression.Add(PersonFields.TheKey == thePerson.TheKey);
using (DataAccessAdapter adapter = new DataAccessAdapter())
{
adapter.UpdateEntitiesDirectly(thePerson, filter);
}