Steps to Reproduce:
my-custom-element.js
class MyCustomElement extends HTMLElement {
static get is() {
return 'my-custom-element';
}
}
customElements.define(MyCustomElement.is, MyCustomElement);
my-custom-element.html
<script>
class MyCustomElement extends HTMLElement {
static get is() {
return 'my-custom-element';
}
}
customElements.define(MyCustomElement.is, MyCustomElement);
</script>
F2 in both files:

With the same code, the "Rename Refactoring" doesn't work in HTML language.
Rename is currently not provided inside embedded JavaScript. But you can use 'Change occurrences'
It could be great to have the same behavior inside script tags than we have in JS files. Like this one @abdonrd days and jsdocs comments per example.
Most helpful comment
It could be great to have the same behavior inside script tags than we have in JS files. Like this one @abdonrd days and jsdocs comments per example.