Learn Swedish: Regeringen utnämnde henne till ambassadör. - The government appointed her ambassador.

In Swedish, verbs of appointment (like utnämna to appoint, or välja to elect) and transformation (like göra to make) require the preposition till to indicate the new role. While English often places the person and the title right next to each other, Swedish needs till to link the person to their newly acquired position.

Why is there no article before ambassadör? Shouldn't it be till en ambassadör?

You should use the bare noun here. Just like when stating someone's profession (e.g., hon är läkare), Swedish drops the indefinite article (en or ett) when referring to a title, profession, or role. Following till in an appointment, leaving out the article emphasizes the abstract rank she is stepping into rather than treating her as a countable object.

If she was already working in that role, would I still use till?

No, till is specifically used to show a change, transformation, or appointment into a new role. If you want to describe a role she is currently holding, you use som (as): Hon arbetar som ambassadör (She works as an ambassador).

Is utnämna the standard verb for giving someone a job?