I see the current pope's real middle name is the previous pope's papal name. Has this ever happened before?

It does not appear so. Popes until the late tenth century used their birth name. The first appearance of a middle name for a pope occurred in the fourteenth century, although middles names didn't occur with great frequency until the 1500s. Another limiting factor was that most of the common names chosen by popes were not commonly used by people. Pius, Innocent, Boniface are examples.

Although this was not asked by the original question, the birth name of Pope Paul VI was Giovanni, the name of his predessor Pope John XXIII.

https://en.wikipedia.org/wiki/List_of_popes

Small addendum (not really an answer): While it is actually rather common for Europeans to have multiple (often way more than 2) given names, it's unusual to actually use more than the first - that "middle name" convention is mostly an American thing.

King Charles III for example has four given names - Charles Philip Arthur George, All but the first would be "middle" and he could actually have chosen to reign under any of the four, but he is rarely referred to as anything but Charles.

It is thus possible (although not particularly likely) that a pope may have had a second, third or further given name that matched the regnal name of a prior pope or even his direct predecessor. We'd just not know - for many pre-20th century popes, their additional given names may not be recorded at all. Leo XIV is the first pope for whom this name coincidence it is definitely known.