Yes, the conversion of DC to AC is done by an inverter. Just use a transistor arrangement to configure an astable multivibrator, then you can amplify the signal, and pass it on to a transformer. In case you dont know how to configure the astable, just google it and you will get it.
There is a type of oscillator popularized by the name 'joule thief', which can extract juice from a battery that is drained below 1V, and drive a bright white led (which requires 3.6V).
Its name is blocking oscillator. It's made from a handwound transformer using a small core. Typical operating frequency is 10kHz to 100 kHz.