Where are hearing aids manufactured?

It depends on the manufacturer.  Starkey, for example, is an American-based company that manufactures their devices in the United States.  Oticon, ReSound, Wydex, and a few others originate from Denmark.  There are hearing instruments produced in many other countries as well.  However, almost every one of them has a state-side office where their instruments can be serviced and custom earmolds can be created.

Hearing instruments are manufactured in many different countries in almost every continent.
3D printing and impression scans mean you can be prescribed aids in England but the manufacturing might be done in Poland or Singapore.

Hearing aids use DSP chips which all most entirely come from Asia; in the case of hearing aids a lot of the DSP chips come from China, Taiwan and Singapore. The exterior shells can be printed anywhere in the world as 3-D printers can be used; especially in the case of ITE (In-The-Ear) hearing aids. Romania and Germany are places that some other hearing aid parts come from. Some of the wire/ receiver portion of BTE (Behind-The-Ear) hearing aids are made in Germany. Some of the hearing aid chargers and remote controls come from Romania. There is some variance per each manufacturer.

All of the major hearing aid manufacturers have state-side manufacturing facilities.  However, a lot of their "home bases" where the instruments and their parts originate from, are in Europe.  There is one manufacturer whose home base is here in the states but all the other major manufacturers headquarters are in other countries (primarily Europe).