Describe the bug
#247 introduced the ability to mutate tools, prompts, and resources, but the way updating by name/uri works is buggy in that it captures the original identifier and continues using it, even if it's no longer the correct one. This means that updating e.g. a tool name more than once leads to incorrect behavior.

To Reproduce
Steps to reproduce the behavior:

1. Register a tool by name - let's say "Foo"
2. Call foo.update({ name: "Bar" }). This works well and we remove "Foo" from registered tools and add "Bar".
3. Call foo.update({ name: "Foo" }) - trying to return to the original name. This has no effect because the check updates.name !== name returns false, since name is the captured original name (Foo) rather than the current tool name (Bar).
4. Alternatively, if we call foo.update({ name: "Baz" }), we end up with calling delete this._registeredTools[name], which tries to delete Foo, which is anyway no longer present in _registeredTools, and then adds Baz, ending up with both Bar and Baz in the _registeredTools collection.

Expected behavior
Updating a tool/resource/prompt identifier should compare the new identifier to the current one, rather than the original one.