Traditionally, in the days of prints, a headshot would be cropped 10” x 8", and this is the way that headshots in the UK have always been cropped.
However, the way we use headshots digitally and the use of the internet, it leaves a lot more scope for different cropping. For example, some people are shooting in the UK what they call 'the US style' of headshot that is becoming ever more popular, and is shot in landscape rather than portrait orientation, this can still allow for a 10 x 8 crop, but also can be used for websites and business cards as well.
How your photographer crops is down to them, as they will always crop the shots to how they feel works best for each photo. Some photographers offer a cropped and un-cropped versions, so worth checking before booking.
Worth noting that cropping your headshots yourself (image manipulation) is an infringement of copyright in most photographers terms and conditions, so worth looking at before you attempt to crop an image.
See our post on copyright here