How to suppress validation when nothing is entered

You can change your person class to fire validation error only if Name property was ever changed:

public class Person : IDataErrorInfo {

    private bool nameChanged = false;
    private string name;
    public string Name {
        get { return name; }
        set { 
            name = value;
            nameChanged = true;
        }
    }

//... skipped some code

    string IDataErrorInfo.this[string columnName] {
        get {
            if(nameChanged && columnName == "Name" && string.IsNullOrEmpty(Name)) 
                return "Name is not entered"; 
            return string.Empty;
        }
    }
}