You’re right in your second point, at least. Whatever you develop out of the thoughts of Agile won’t be called Agile. It is its own thing, with whatever new name you decide to give it.

You can build your own processes around Agile principles. As long as you don't carve the processes in stone and revisit them you still can be Agile.

Reading the principles of Agile does not make what you're doing Agile any more than reading the words of the bible makes what you're doing Bible, even if you took something useful out of that reading. Whatever it is you end up doing is what you decide to call it.

Agile is more like a checklist of things to remember if you're going to operate without managers. Like, stay in touch with the business people, keep your work available for other developers to see, work with people who can be motivated without a manager hovering over them, etc. All obvious when you think about what role managers fill and what you need to do if they're gone, but still a decent reminder if you're serious about going down that road.

It's not something you do, rather something you can think about if you've decided managers aren't the right fit for your project.

Did you mean to respond to someone else? I for one never said anything about reading Agile principles making anything Agile.