How to distinguish clients with the same name under the same organizational structure?
Please can you give more context.
Are you using the Cloud Technology?
Typically it is not possible to distinguish clients with the same name under the same organizational structure.
Following best practice, users would create unique subfolders for each client under the main "Customers" folder to organize them and make them easier to differentiate.
Its not too late to introduce this concept.
However depending on what your subscription package with us is, you could try use custom fields at project level.
Custom fields represent the additional set of values that can be added to project templates or projects in order to filter and group them. They can be configured from Resources > Custom Fields and support various field types such as number, boolean, text, etc. They can also be used in project templates, during project creation, or when editing an existing project. Additionally, custom fields can be associated with customers to help filter them faster.
I hope this helps