No one decides what an opening or opening variation is called. Kasparov made the move immensely popular in the early 1980s. But he didn't invent it. And many others have used it before him. Including Petrosian in the 1960s. So use the name you like. And prepare yourself for the fact that whatever name you use, you'll probably have to explain what you mean: the 4.a3 variation.
4.a3 line in the QID
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Is the 4.a3 variation of the QID called the Kasparov Variation or the Petrosian Variation? Many books call it the Kasparov Variation, while Chess.com lists it as the Petrosian Variation.