My experience is that sometimes street names are dropped in favour of a clearer/more succinct direction. 'Take the 2nd exit onto the A37' is probably preferable to, say, 'Take the 2nd exit to xxx Road, and then enter the A37'.

Easier to simply look for 'the 2nd exit' and not have the directions convoluted with unnecessarily long and detailed instructions which are of no real help and may in fact confuse the situation rather than make it clearer particularly when taking into account that there is a finite time which is dependent on the vehicle speed and cognitive ability of and subsequent response by the driver, in that there is limited time in which the driver needs to hear, process and act on the voice directions, [blah blah, blah blah] ......
exactly as illustrated by the preceding overly long and pedantic sentence! i.e. If you mean that you are usually getting spoken street names, your one example is as Garmin intended.