Tom Riddle, sucumb to the wishes of Muggles? Ha. No, he didn't register. He didn't cooperate at all.
But, it really didn't matter whether he did or not. He was a minor when he was first Ported in; they knew about him, knew his name, and someone high up had children who once upon a time had read a certain book series about a teenage wizard saving the world. They knew who he was anyway. They knew what he could do. And there were a few unsolved murders someone higher up decided he must have been responcible for (he wasn't, of course, he'd covered his own tracks much more carefully than that, always leaving someone responcible). Once it was clear he wasn't going to cooperate on his own, they came after him.
Not that it did them much good. He was already an expert in mind magic of various sorts, and they hadn't yet figured out how to keep him from Apparating without shutting down all his magic, which they could never seem to do. For almost two years, anyone sent to apprehend him would mysteriously forget what they had come to do, or his name and what he looked like, or their names and backgrounds...on a couple occasions, he sent them back with some random Muggle they were now absolutely convinced was him. He was careful to never kill anyone; they were adamant enough without any evidence of him doing wrong.
And of course, he didn't spend those two years just sitting around, waiting for the next goverment official to show up. He revived and perfected his wandless magic skills. He made a second Horcrux and hid it halfway across the world (his first was already hidden somewhere in the City). He learned whatever magic Bellatrix would teach him, Dark or not. He learned more about the Muggle world and their technology than he'd ever cared to know but was now necessary.
Four years to the day he arrived in the City, he left Bellatrix some very specific instructions on what to do with his possessions and a promise to return, and then Tom Marvolo Riddle disappeared.
And he stayed that way for several years, as he traveled the world and continued with his studies as best he could when dealing with Muggle "magic." It gave him enough ideas for his own spells and potions to be useful, and he didn't have the government breathing down his neck, which was more than enough reason to do it.
The first few whispers of Lord Voldemort began after a couple years of this. While he was careful to only practice his more vicious Dark magic in remote areas, he did not make his presence a complete secret, nor who he was. Not long after that, Voldemort appeared on the hacked imPort network--only a couple times, months apart, and only for a couple posts at a time, but it was enough to prove the he was still alive and out there.
Also around this time, a blog by someone named Ophiuchus appeared, decrying the actions of the US goverment and others and being generally very pro-imPort. Well spoken and well argued, Ophiuchus quickly gained a following among civilians, quite a few of whom ensured his blog stay online when various groups tried to shut it down. Even later entries, which gradually became almost too pro-imPort and began advocating violence against the opressors, didn't seem to drive many people away.
The timing was a little too close to be a coincidence, but if asked, Voldemort would never admit to also being Ophiuchus, although he did think the man had the right idea.
And then, Voldemort and Ophiuchus went silent. Because everything went wrong.
It was ridiculous really, how it happened. Such a Muggle way to die. One of the smaller, more fanatical anti-imPort groups connected a few dots and tracked him down, to get rid of him. He managed to block most of the bullets and killed almost everyone who attacked him. But he didn't count on them having a way to counteract his magic. So the last few bullets hit, and they hit vital places.
Every single one of them would mysteriously end up dead later, with no clues as to who did it.
It was ridiculous, but they didn't succeed in killing him. His body was dead, but Voldemort was still alive, and he could possess others and use their bodies instead. And he quickly discovered that while he couldn't use all his magic in another body, he could use some of it, so he wasn't completely helpless. His presence did considerably shorten the lives of anything he possessed, however, and using his magic made it even worse. But still, he was alive.
He spent another year jumping from body to body, never staying in one place for long, to make sure he was believed to be dead and no one would come looking for him. Then he headed back to the City to enlite Bellatrix's help in returning him to his own body and join in the resistence movement. Because like hell is he going to let the Muggles get away with this nonesense for much longer.
Aaaand around this time Voldemort and Ophiuchus both show up online again. Ophiuchus with a grand tale about how he's had people try to murder him just for writing things that's intended to incense people. Voldemort with information about various private goings on.
And yes, he still has Harry's his wand, it's just stashed away somewhere where he won't lose it.
And yeah, he'll be out there doing things whether he's in his own body or not. And he's probably been back in the City at least a year. And infiltrating things and charming information out of people.
and someone should tell me to stop adding things to this it's long enough already