I read in a book it's called a
oven stove element, and I used this word. But it might sound formal, is there another more common name for it? If not, what else is it called?
That is not an oven element, it is a stove element (or, sometimes, burner element, stove-top element, or stove-top burner element). Informally, it may be referred to as a burner; as in, “Put the kettle on the burner”. (At the stove-elements link above, if you click “Related searches: oven element” you can see pictures of oven elements.)
In general parlance, I think it is fairly safe to just call it 'the stove'. I'm not suggesting that this is the correct name for that particular spirally object, just that most usages would not need the precision of mentioning a particular element - for instance if you are requesting someone to heat the kettle, you don't usually care which element they use, if you're asking them to remove a boiling saucepan, it is going to be pretty obvious which pan needs to be moved.
To illustrate: 'Can you put the kettle on the stove element?' sounds a lot less natural (to me) than 'Can you put the kettle on the stove?' (Actually, bad example: you would just say 'Can you put the kettle on?')
You need only refer to the element if you need to differentiate. For example: 'Can you put the kettle on the left front stove element - the right element is broken'.