Whitebeard get the "world strongest pirate" title because he was the only one on par with Roger and after Roger died there was nobody even close to contest his title despite him growing older and sick.
The previous holder, if any, could have been Roger or even before that most likely Xebec. We know Roger is also the only one who has been labeled with the title "great pirate" so far.
Mihawk imo get his title in a fashion similair to WB. He was the best along with another man, Shanks: their duels, with the title on the line as a collateral, shock the grand line. Then Shanks went out of the picture because he lost his arm and Mihawk was left without any valid competitor for the title just like WB after Roger died. To this days we can see a bored Mihawk waiting for a valid rival, his hopes are on Zoro who most likely will be the next holder of the title.
And last we have Kaido, he got his "people say, "in a one on one fight, always bet on Kaido" land, sea and air - out of every living thing in the world this pirate is said to be the strongest creature alive!!!" box which is not a title but what people (in Op world and not only) believes to be true. This because that even if people in OP world would always bet on him we readers know that if we bet on him when he fought Oden or BM (and maybe Shanks too)(there are also the 7 defeats to still discover completely, we have just a few of these) we would have lost our money both times (if we exclude external intervention and use of hostages or a tie like it happened with BM).
So I will talk about his real title: "king of the beasts", he got this title because he is either the strongest zoan user, has the best zoan or because he leads a crew made entirely of zoan users or most likley a combo of all these 3. The next one to get the title could only be his son, King or Queen if he gets defeated and his crew goes on. I doubt any other pirate will ever start a project like Kaido (crew full of zoans and the captain is the strongest zoan df user and has the storngest zoan). Most likely there was not any previous user since the peculiarity of this title.