Different languages have different set of features and also differ in implementations of those features.
Properties in general are a tool that provides additional level of abstraction around encapsulation and enables future implementation changes while preserving stable public API.
Some of the benefits are more visible in some languages than the others. For instance, if you have public field Name and you want to add some code around retrieving that field is easy to do in Delphi. You can rename field and move it to private section and declare public function Name to retrieve it. I Java, you cannot do such thing because calling method must include brackets. This requires refactoring all code that uses such field. If you want to add setter, you will break the code in any language.
This is where using properties helps with encapsulation. They hide unnecessary implementation details and give implementing class to ability to change those without breaking user code. You can start with simple field backed property, which from performance aspect is no different than public field and you can add getters and setters as needed without breaking code. Without properties, you can also maintain stable API, but the cost is having getters and setters for everything and paying the price in performance. No matter how small it is, eventually it can add up.
Additionally, code with simple assignment is easier to read than setter method.
There are some parts of general properties functionality that Delphi does not implement, like different access levels for reading and writing, or some additional ceremony when declaring properties, especially in interfaces. Some of those could be improved to make properties more flexible, but lacking them is poor argument against using properties. In situations where you really need some functionality properties don't provide, you can use other ways to achieve what you need, but not using properties everywhere else because you cannot do something in rare occasions is also not very convincing argument.
Arguments around name refactoring are not very convincing either. They compare name refactoring, where there is a bit more renaming in declaration. Now, compare that single place where you need to make additional rename, to refactoring all code in case where you need to replace public fields with accessor methods.
When it comes to extra declaration code needed for properties with accessor methods comparing to only having accessor methods, think how much unnecessary getters and setter methods you need to write in cases where you could use field backed property declaration.
Overall using properties results with cleaner code and having more functionality than you can have with simple fields or just accessor methods. The little bit of ceremony around the declaration is price I am more than willing to pay, to get all other benefits.