How can organizations make automation feel to customers like it was designed primarily for them?

I'll respond in two parts:

1: Combine detailed customer data with the automation.

2: To William Sovie's point, design the technology for the customer.

1: Use detailed customer data to personalize the experience that is delivered by the automation.

Example: Mrs. Jones has a business account at a bank. Every weeknight, Mrs. Jones makes a cash deposit between 7 and 8 pm. The bank knows this, because it has the transaction data, along with personal information (name, and preferred language) and business data about Mrs. Jones.

When Mrs. Jones enters her bankcard into the ATM machine at 7:30pm on a Tuesday night, the ATM should immediately flash, “Good evening Mrs. Jones. Would you like to make a deposit?”

While the base technology (The ATM machine and the software behind it) is not designed for any particular customer, the integration of customer data to the base automation results in a highly personalized experience for each customer.

2: To William Sovie's point, design the technology for the customer. One way to do this is by asking the customers what they like, dislike, and prefer, as William says.

But look beyond what the customers explicitly request, because customers only know what they know. There may be other forms of automation that will deliver the desired experience; automation that the customer is not aware of.

The customers will recognize an automation system that is making them more efficient and allows them to work in the manner they would like to, though change is not easy and they will often need some incentive to use the new systems. Once they start using the new systems, if the systems do serve the customers, they will appreciate those systems.

The difficult questions are:
1. What automation would best serve the customers
2. How to get the customers to embrace the change and use the new automation

I suspect each manager knows their customer's pain points and knows what automation would best address their needs, but generally speaking, things that make the customer's tasks more efficient and things that allow the customer to work as best meets their style addresses the customer's needs. Knowledge bases are the classic example of this. Customers can often get their answers directly out of a well designed knowledge base faster than having a support engineer search for them. Many customers also prefer not to work with a person to get their answer.

To get customers to start to use new automation generally requires some incentive to change their work habits. Sometimes the automation is so clearly an improvement to the customers they will not need any additional incentive. Other times, I have given the customers additional capabilities through the automation that have not been available through the traditional systems. I also make sure the customers continue to have an option of which path for at least a transition period. A choice will keep the customer from feeling they are trapped into using the new system. Instead of resisting the new system, they will take the time to evaluate which will work best for them. I have the support engineers let the customers know about the benefits of the new automation when they call up with the traditional system.

In the end, the new system has improved the customer satisfaction and improved the efficiency of the delivery of the service.

Your question sounds like there is an existing automation system for customers,
nonetheless, to make it feel customized... customer research should be continuous.
Whatever pertinent details you get from the market, apply it to your system.
Sooner or later, the system will be applicable to almost every customer.

Just bear in mind, time is gold.