I don't know the English name, but I remember a similar trick used to replace a triac (the circuit was called magnetic amplifier in that old schematic, but Wikipedia shows something slightly different for "magnetic amplifier").
The idea in that old article was to use transformers in series with a load, as switches (because triacs/thiristors were rare/expensive back then). The load was 220Vac light bulbs in series with 220Vac transformers, and in order to turn on the light bulb, a low voltage (transistor) was shorting the secondary of the transformer. When a transformer is shorted, the current rises through its primary coil series with the load, too. Same with auto-transformers (as in the OP cropped schematic).
A larger schematic, or the destination of that schematic/device might be helpful to guess correctly.
Otherwise, that symbol is probably an auto-transformer (which is a dual 600mH inductance coiled on the same magnetic core).
My guess is the 2x600 mH is used as a magnetic (amplifier) switch, in a similar manner as explained before. Some load is in series, and when one half of the coil is shorted, the series load will get AC current.