A wide variety of names have been used for diamonds that have been made by people. In the early days, the names “synthetic diamonds” and “man-made diamonds” were most often used. Synthetic diamonds was the more scientific name and the name used among technical people. Man-made diamonds was a name used by much of the general public.
Until recently the name “lab created” was used much more often than “lab grown”. In December of 2013 the number of people using the name “lab created diamonds” as a Google search query was rivaling the use of “man made diamonds”, which was the dominant search query for these materials at that time. In February of 2017 “lab created diamonds” became the clearly dominant query. (You can see this history for yourself in the graphic above.)
Then a major shift hit the language of Google search queries. In June of 2018, “lab grown diamonds” shot up to the leading position. This date is coincident with the first appearance of heavy online advertising for the Lightbox diamond brand of De Beers. Their ads and their website clearly used the name “lab-grown diamonds.” Their product launch most likely changed the language being used by people searching Google. It also caused a major increase in the number of people who queried Google for information about diamonds made by people.