I think one of the most difficult things is to follow the footsteps of a famous father into their same field, especially when their father is an icon. In the US, we had the example of Pete Rose's son Pete Rose II, who toiled in the minors for over 20 years but only briefly made the majors (and that was mostly a publicity stunt by the Reds). In Japan, the biggest example is Kazushige Nagashima, the son of Shigeo Nagashima.
Kazushige was born in 1966, during the height of his father's popularity (and near the beginning of the V9 Giants run). Like his father, he attended Rikkio University of the Tokyo Big Six league, becoming team captain despite only hitting .225 during his career there. He was drafted in the first round of the 1988 draft (as always I feel compelled to mention that this was held in the fall of 1987) by both the Swallows and the Taiyo Whales and was awarded to Yakult in the lottery. Other players chosen in that round of that draft were Kazuyoshi Tatsunami, Hideki Irabu and Ken Suzuki - all players who went on to much more successful careers in NPB than Kazushige did. The Swallows assigned Kazushige the uniform number 3, the same one that his father had had.
Kazushige spent four years playing for the Swallows. In his best season, 1989, he hit .250 with 4 home runs and 15 RBIs in 69 games. He never played in more than 88 games at the ichi-gun level, doing that in his first season in 1988.
In 1992, it was time for a change. Shigeo Nagashima and Yakult contacted the Dodgers and asked if they could arrange for Kazushige to spend the season with the Dodgers Class A team in Vero Beach in the Florida State League. Vero Beach had previously hosted some Japanese players in the late 1980's (most significantly Masahiro Yamamoto of the Dragons). The Dodgers agreed and Kazushige played 79 games with the Dodgers, hitting .235 with 7 home runs and 26 RBI.
In 1993, the Giants brought Shigeo Nagashima back as manager for the first time since 1980. Yakult sold Kazushige to the Giants so that the father could manage the son. Kazushige had less success with the Giants than he had with the Swallows, batting .216 in 1993 and .172 in 1994. He missed the 1995 season with an injury and hit only .143 in 1996. He then retired. He has had a number of jobs since then, including actor, and baseball commentator and I think he now has some job in the Giants front office.
My impression has always been that Pete Rose II never had any plans for his life other than being a baseball player. You read old books and articles from the 1970's and 1980's about his father and there's frequently a mention of how Pete II is just like his dad. Pete II is now a minor league manager so perhaps it is finally coming together for him but it's been a long road with some ugly stops to get here (including a jail term for PED distribution).
I'd be curious if it was the same case with Kazushige. I think he had the advantage of deciding that the baseball thing was not working out at age 30 rather than continuing to keep trying. He also was much better paid than Rose was, so he had more options. He also still had the advantage of who his father was, which I think charitably has not been much help for Rose beyond the name.
For those that are curious, Kazushige appears in the 1992 Classic Best Vero Beach Dodgers team set. Here is his 1992 BBM card (#123), produced by the company despite the fact that he didn't make any appearances with the Swallows that season: