To clarify, yes, you need to set default values in the constructor for class derived objects. You will need to ensure the constructor exists with the proper access modifier for construction where used. If the object is not instantiated, e.g. it has no constructor (e.g. static methods) then the default value can be set by the field. The reasoning here is that the object itself will be created only once and you do not instantiate it.
@Darren Kopp - good answer, clean, and correct. And to reiterate, you CAN write constructors for Abstract methods. You just need to access them from the base class when writing the constructor:
Constructor at Base Class:
public BaseClassAbstract()
{
this.PropertyName = "Default Name";
}
Constructor at Derived / Concrete / Sub-Class:
public SubClass() : base() { }
The point here is that the instance variable drawn from the base class may bury your base field name. Setting the current instantiated object value using "this." will allow you to correctly form your object with respect to the current instance and required permission levels (access modifiers) where you are instantiating it.