Data wise, TID/SID isn't known to be generated based on OT.
It's legal when you catch the mon in the correct area, and leave the caught data unchanged (for the most part).
Long story short, we know how the games calls the EC, PID, IVs, HT, WT sequentially.
These values are all called from the same RNG seed.
While it's presently not implemented into PKHeX, cause the checks for it are not immediate (takes like 30 seconds to a few minutes),
it is possible to be manually checked.
[We basically take those stats, throw it into a program, and see if it returns a seed]
If you edit anything incorrectly, it breaks the correlation, and we can tell it's hacked. [basically at this point, no seed is returned]
(Same thing occurs to mons with PID type overworld8, except it is a lot faster to check, and PKHeX checks for it)
Yes and no.
If the mon doesn't bear any PID type, then it'll still be legal.
If the mon bears a PID type (like Overworld8 mons), then it won't be legal.
Also, keep in mind that changing any stats, could be legal at the moment, but illegal in the future, which means the edit was never legal to begin with, just that people didn't know.
Case study: editing overworld8 mons were thought to be legal 1 year ago, cause at that point overworld8 was not discovered.
Anyhow, as of now, to be safe, it's fine changing OT/TID/SID, but not everything else. Overworld8 type details.
(Also, it is RoC, not RoG. ReignOfComputer, not ReighOfGomputer)
Just write in random numbers. If you're so concerned about it, start a new game, then take the numbers generated by that save.
As of now, there is no known correlation regarding the TID/SID generation.
Catch the Pokémon yourself
In all seriousness, just changing the OT/TID/SID is probably enough.
Without hacking and viewing the data, it's not like people will see the PID/EC pair.