Well, if you want randomness, the game can give you that. Just create a player, give him a new name, and then let the game do the rest. Most youngsters in OOTP - even ones with a great deal of potential - don't end up in the majors. That, of course, is just like real life.

So (just in case this is of interest to anyone other than me), I have for the moment settled on an approach that involves randomness but is not completely hands off.
What I have done (or am working on) is a process involving the following steps, which has allowed me the fun of creating some charts and incorporating the beloved 20-sided die plus the use of online random name and number generators:
Step 1: Identification of which current players will have relatives created in this universe. For now I will use a random process to identify two current players per season who will have a relative in the W.P. Kinsella League universe.
Step 2: Identify what type of relative is to be created. Since I am randomly identifying whether the relative will be a contemporary (brother, cousin) or next generation relative (son, nephew, son-in-law) or even two generations in the future (grandson) this does not mean that two new players will be created each year but just that they will be identified, often for future creation. As the league progresses I will watch how this works and might alter Step 1 to have fewer new players identified if necessary.
Step 3: Identify age of created relative at Step 1- this will often be a negative number indicating that a relative will be created in 5 years or 15 years, etc.
Step 4: Identify month and day of birth using charts I created.
Step 5: Identify primary position of player to be created (die roll, charts.)
Step 6: Identify the type of player to be created (Player Type Chart-more about this below!)
Step 7: Based upon Step 6 above, use random number generator to identify player template used for player creation (again, more below.)

When I refer to type of player I am perhaps even referring to archetypes. I created a list of pitcher player types and position player types and from these will then be creating a number of ratings/personality type/etc. templates to choose from for each created player. For pitchers my player types (at this point) are 1- Flame Thrower 1 (control struggles) 2- Flame Thrower 2 (hard but straight FB) 3- Control Artist 1 (junkball pitcher) 4- Control Artist 2 (corner painter) 5-Deceptive and consistent (side-armer/submariner) 6- Deceptive and inconsistent (knuckleballer, primarily) 7-Lifer (mediocre to poor talent, future pitching coach/manager) 8-Workhorse 9-Steady Eddie 10- Super-Star! Some of these are probably pretty self-explanatory. Basically #1 will have great velocity but be very wild, #2 will have great velocity but very poor movement, #3 will throw decent off-speed stuff but very mediocre velocity, #4 will throw okay fastball with not great velocity but with very good control and probably decent movement, #5 and #6 are more about arm angle and pitch type, #7 is intelligent leader with low ability who will perhaps one day be coach and/or manager, #8 is average to below average starter who can eat innings, #9 is average to below average reliever who is durable and has stable personality, #10 is, well, obviously, the guy who could become a great to HOF type player.

For position players I am creating the following types: 1-Speedster 2-Defensive whiz 3-slugger (1-tool mostly) 4-Utility man 5-Mr. Steady 6-Scrapper 7-Lifer 8-Walking Man 9-Super-Star! Again, mostly self-evident. First guy has good to great speed, base-stealing and base-running ability and not a lot else. #2 is very good to great defensively at at least one position, #3 is great power hitter but has big weaknesses elsewhere, #4 is stable, multi-positional player with decent defense and not entirely atrocious bat who could fill a role, #5 is potentially average major league player, #6 is firebrand (think Billy Martin), #7 is probably below-average to poor player with high leadership, high work ethic, high intelligence and has good chance to be future coach and/or manager, #8 has a great eye and good to great avoid K but not a whole lot more, #9 is well, you know.

A note about the Super-Star category: this will require a roll of 20 on the 20-sided die but even then this guy actually developing into a true superstar should be rare as I will be building the templates for this type with most of them having some potentially serious flaws that could and probably will restrict their development. None of the other categories should have much chance of having significant major league careers other than possibly some of the Mr. Steady position players or Workhorse and Steady Eddie pitchers.

I suggested something like this as a low priority request/idea for a future version. My thought was a field in the player editor for family relation (son, brother, nephew, etc). My thought was more that I wanted to see any relations to the owner be more sought after (drafted/untouchable in trades).

In my past leagues - fictional - I have often created the 3/4/5 variant of generations. I'd also indicate in their player history if they were related to some other star, but that got tedious over time. It was still fun when there were a few prominent baseball families in my fictional leagues over time.

Wanted to revisit this thread due to something I found while going through the just released draft list for my W.P. Kinsella League.
Spotted a kid named Chris Cardin, Jr. among the players eligible for the draft. Now, as it happens, Chris Cardin is the name of a player who was a star in the WPK who retired at the end of the 1967 season. We are now in May of 1969. Chris Cardin is 42 years old. Chris Cardin, Jr. is 18 years old.
Gotta be father and son, right?

But I didn't create this player. He is not part of the process I am using to add relatives of current WPK players to the WPK universe. The game made this guy.

Is this something that happens in OOTP Fictional leagues? This can't just be some crazy coincidence of naming, could it?
If this is built into the game, that makes me so happy.

I'll still be adding relatives, including brothers, cousins, and grandsons, but I love that the game seems to be creating the occasional junior.

It does appear that the game is creating some family lineage. ;)

Yep, this is something built into the game :)

Nice!
I'm sort of glad I didn't know about this beforehand so that it could be a fun surprise.

OOTP used to do Jr. for fictional players, then sometimes you'd see Jr. Jr. which obviously was a bug, but no longer. Now just fictional Jrs happen at times.

I often create generational players for my leagues, and when they go on for 100s of seasons, it's not odd to see III, IV, V players from time to time.

I had one series of families where the greatest player of all-time had so many legacies that another family name (via his great granddaughter) spun their own dynasty. It's a lot of fun for me and a good way to remember certain players.

I move pretty slowly with this particular save and am only entering the sixth season of play now. But already I have a few cousins/brothers of current players who have entered this baseball universe through my created players process and I'm finding it great fun.
I actually ended up drafting the game-created Jr. I referred to above. He isn't much of a prospect and will probably never make it to the major leagues but I didn't draft him prematurely- at some point he was just basically the best player available and it was my turn, so what the heck.
The process I built for creating legacies is quite random. I can only hope that over time it will spawn at least one multi-generational (beyond father and son) family of ballplayers.

Speaking of Jr. Jr.- there is an indie rock band out of Detroit by that name. They used to be called Dale Earnhardt Jr. Jr. Neither here nor there, but I think it's kind of funny.