1. I would like to know why in ISO 27001 there is a "Supplier Management" and there is no "Customer Management"?
Please note that ISO 27001 main objective is to protect the information, that belongs to the organization or is under its responsibility (e.g., customer information, partners information, etc.).
Considering that, the information to be protected may be accessed by suppliers (e.g., a SaaS provider, contractors, etc.), and the organization needs to ensure that information is also properly protected by suppliers (by means of contractual clauses, periodic service review, etc.), thus the need for “Supplier management”.
Now, customer management involves much more than information protection, so to include it in ISO 27001 would mean an unnecessary overhead for the information security management system.
2. How should I align or assure my clients within my implementation of ISO 27001?
For alignment of customers' interests and requirements with your ISO 27001 implementation, you must consider them when working clause 4.2 Understanding the needs and expectations of interested parties. Fulfilling this clause is enough for the standard to consider customers in your implementation.