There could potentially be such a concept explored in fanfiction. Since Jojo has such a rich and complex world with concepts like time - related stands, it's not far - fetched for fans to create their own stories about traveling back in time within the Jojo setting. But as of now, no official Jojo novel focuses solely on this time - traveling aspect.
Well, in such a novel, the time - traveling aspect would open up a whole new dimension of storytelling. The author could explore the origins of the stands in more detail by having the character go back to the time when stands first emerged. There could be intense battles with historical versions of enemies. The character might also face moral dilemmas, such as whether it's right to change the past even if it means saving lives. It could be a thrilling adventure filled with mystery, action, and the unique Jojo - style humor and drama.
One interesting concept could be the interaction between different generations of JoJo characters in the same time period. For example, seeing Jonathan Joestar meet Giorno Giovanna and how their different values and abilities would clash or complement each other. Another concept might be the alteration of key events in the JoJo timeline through time travel, like preventing Dio's rise to power in a different way. Also, the exploration of how Stand abilities could be used in time - travel - related scenarios, such as using a Stand to repair a disrupted timeline or to foresee the consequences of time - travel actions.
There's no way to really tell if it's common specifically for someone named Jojo. However, in general, reading fanfiction is a popular activity among fans of many different franchises. The Jojo series has a large and dedicated fan base, so it's likely that there are fans named Jojo who partake in reading fanfiction, but we can't say for sure how common it is without more data.
Perhaps this Jojo is interested in exploring different interpretations and stories within the Jojo universe that fans have come up with. Fanfiction often takes the existing characters, settings, etc. from the original Jojo series and creates new and unique storylines. So, this Jojo might be a big fan of the series and wants to see what other fans have imagined.
Jotaro Kujo is quite popular. His strong and stoic personality makes for interesting interactions in different time periods. Dio Brando is also a common choice. His villainous nature and powerful Stand, The World, can create a lot of chaos when time - travel is involved. And then there's Jonathan Joestar. His noble character can be a great contrast to the more modern and complex characters when he's brought into different timelines through time travel.
It depends. Maybe there are some telltale signs or elements that suggest it's a JoJo reference fanfic, but without specific context, it's hard to say for sure.