Browsers follow a defined priority order, the accessible name and description computation, to decide which of several possible sources (aria-labelledby, aria-label, a form label element, alt text, or visible text content) wins when more than one is present. Understanding this order matters because it explains why adding an aria-label to a button that already has visible text can accidentally override that text for screen reader users.
Every interactive element needs a non-empty accessible name; buttons and links with only an icon and no text or label are a very common audit finding.