action.setTitle()

details

object. The new title and optionally the ID of the tab or window to target.

title

string or null. The string the browser action should display when moused over.

If title is an empty string, the used title will be the extension name, but action.getTitle will still provide the empty string.

If title is null:

• If tabId is specified, and the tab has a tab-specific title set, then the tab will inherit the title from the window to which it belongs.
• if windowId is specified, and the window has a window-specific title set, then the window will inherit the global title.
• Otherwise, the global title will be reset to the manifest title.

tabId Optional

integer. Sets the title only for the given tab.

windowId Optional

integer. Sets the title for the given window.

• If windowId and tabId are both supplied, the function fails and the title is not set.
• If windowId and tabId are both omitted, the global title is set.

This code switches the title between "this" and "that" each time the user clicks the browser action:

function toggleTitle(title) {
  if (title === "this") {
    browser.action.setTitle({ title: "that" });
  } else {
    browser.action.setTitle({ title: "this" });
  }
}

browser.action.onClicked.addListener(() => {
  let gettingTitle = browser.action.getTitle({});
  gettingTitle.then(toggleTitle);
});