In the world of project management, if the customer need is the start point of a project. What is the end point in the same context?

Delivering the project outcomes to the customer as per the specifications defined at the start point.

Customer Satisfaction!

The project is not successfully completed untill its delivered to the customer and he acknowledges that it was fully accomplished based on agreement. or otherwise, he will not pay and you may lose a customer and have a bad brand.

Always try to reach two factors , First Customer Satisfaction , Second always be in contact with the customer as he / she will your market media about your product or services any time as long he / she feel that you don't only want to buy or make service but you always follow up if he / she need anything in the future .

For a customer need to be the start point of the project, the fulfilment of the same shall be treated as the closure of the same project.

However as per the current trends, these needs are to be identified and monitored otherwise it can become a never ending project.

Customer Satisfaction, you need to get feed back of the customer after completion to know whether you actually achieved it.

Certainly, Meeting the requirements / Specifications, Customer satisfaction, Meeting Quality, etc help ending the project successfully. 

But, we should not forget that the work of the project manager is not complete here. He Needs to -Document the Lessons learnt, Update the Project Documents (Charter, Proj Plan, Risk registers, etc) to the repository, discuss with PMO team, Send official communication to Vendors (if at all you engaged vendors in your project), get an official sign off on the Project closure. 

Hope this helps. 

Best Regards, Ananth