Sample Code:

List < Contact > conList = new List < Contact > {
    new Contact(
        FirstName = 'Test0', 
        LastName = 'Test0', 
        Department = 'Finance'
    ),
    new Contact(
        FirstName = 'Test1', 
        LastName = 'Test1', 
        Department = 'Technology'
    ),
    new Contact(
        FirstName = 'Test2', 
        LastName = 'Test2', 
        Department = 'Finance'
    ),
    new Contact()
};
            
Database.SaveResult[] srList = Database.insert(
    conList, 
    false
);

for (
    Database.SaveResult sr : srList
) {

    if ( sr.isSuccess() ) {
        
        // Develop code for sucessfully inserted contacts
        System.debug(
            'Successfully inserted contact. Contact ID: ' + 
            sr.getId()
        );
        
    } else {
        
        for ( 
            Database.Error err : sr.getErrors() 
        ) {
            
            // Develop code for failed contacts
            System.debug(
                err.getStatusCode() + 
                ' : ' + 
                err.getMessage() + 
                ' : ' + 
                err.getFields()
            );
            
        }
        
    }
}

Sample Code for existing records:

List < Contact > listContacts = [
    SELECT Id, LastName
    FROM Contact
    LIMIT 2
];

if ( listContacts.size() > 0 ) {
    
    for (
    	Contact objContact : listContacts
    ) {
        
        objContact.LastName = null;
        
    }
            
    Database.SaveResult[] srList = Database.update(
        listContacts, 
        false
    );
    
    for (
        Database.SaveResult sr : srList
    ) {
        
        if ( sr.isSuccess() ) {
            
            // Develop code for sucessfully inserted contacts
            System.debug(
                'Successfully inserted contact. Contact ID: ' + 
                sr.getId()
            );
            
        } else {
            
            for ( 
                Database.Error err : sr.getErrors() 
            ) {
                
                // Develop code for failed contacts
                System.debug(
                    err.getStatusCode() + 
                    ' : ' + 
                    err.getMessage() + 
                    ' : ' + 
                    err.getFields()
                );
                
            }
            
        }
    }
    
}