As I understand it, the phrase 「…」というラベルが付けられているもの literally translates to something like 'a thing with a label reading "..." attached to it'. Unlike in English, there is no verb equivalent to 'labeled'.
That said, this phrase alone seems insufficient to cover all cases that, in English, would use the word 'labeled', where the label is not a distinct object from the thing being labeled. Some other cases have other obvious translations. For example, if the label is directly written on the object in question, something like 「…」と書かれたもの would work. For others however I cannot think of an adequate translation, for example if words have been burned/branded onto an object.
Some alternatives I've considered are 付く, which unlike 付ける seems to include meanings like 'marked' or 'imprinted' as well as 'attached', and 表示する. However, I've been unable to find any examples using either in the way I'd like. I have only seen 付く used to describe things as being marked without specifying what the mark read, and 表示する seems to be limited to things like computer screens, when not being used to mean 'expression' or 'display' in a more abstract sense.
Would either of my alternatives, or some other possibility I've yet to find, do the job? Or am I overthinking either 「…」というラベルが付けられているもの or 「…」と書かれたもの, and thinking that they are more specific in meaning than they actually are?