This is a question of scope. An ontology is complete if it has all the concepts and axioms that are needed. Needed for what? This depends on the intended purpose of the ontology. If you have a local, one-time need to integrate a small number of databases, then you need to include all the concepts that are covered in those databases. On the other hand, if you are building an enterprise ontology to serve as a long-term semantic foundation for your organization, then you will want to focus on only those concepts that are both essential and stable in your organization, that is, the most important concepts: the ones that have been around for decades and will be around for decades to come.
If the ontology has a fairly broad purpose and was not built to be used by any specific IT systems, a good way to check for completeness is to identify a number of possible use cases for deploying it. You might start by brainstorming possible use cases and applications that would solve critical problems that the company currently faces. Focus on those that can be solved by having the right data available. For each use case, identify the goal, inputs and outputs, and the required data to make that use case work. Then check the data requirements against the ontology to make sure they are covered. What is missing might belong in the ontology – making it more complete; or it might be too detailed or application-specific and belong in another kind of model.