From what I have read, his reconquest of the Western Roman Empire and North Africa is outstanding and should be be placed alongside other great campaigns. Why is he such a relatively obscure figure?
But was Belisarius an outstanding general? He was not undefeated like Alexander the Great, his political acumen was nothing compared to Napoleon, and his foes did not write stories portraying him as their most potent enemy as the Romans did for Hannibal. If we look at the contemporary sources, it is clear that Belisarius' reputation was already contested - his secretary Procopius had actively turned against the regime by the 540s and was sorely disappointed by Belisarius' inability to rebel against Justinian, whilst the pro-Justinian chronicler John Malalas outright accused Belisarius of incompetence on the battlefield. Nor should we forget a whole coterie of equally talented men who had helped Belisarius in his wars; indeed it would be men other than Belisarius who finally secured these conquests - Narses the eunuch for instance decisively ended the Gothic War at the Battle of Taginae, and it took a man of John Troglita's calibre to finally defeat the devastating revolts in North Africa, resulting in him receiving a long panegyric celebrating his achievements, the only non-imperial figure to do so in the sixth century. What was Belisarius doing during all of this? He was in Constantinople, out of favour and perhaps embroiled in conspiracies against the emperor Justinian. No wonder his legacy wasn't so glorified!
Belisarius' first victory was against the Persians at Dara in 530, but in 531 he led his army to a major defeat at Callinicum. Interestingly, Procopius blamed the defeat on the leader of the Arab auxillaries, al-Harith, but John Malalas, writing in Constantinople, stated that Belisarius had fled out of cowardice before the battle was even over. As al-Harith's military skills are well-attested to (and Malalas had specifically stated that al-Harith stood firm rather than fleeing as Procopius had described), I see no reason why we should only believe Procopius' account - Belisarius was a good general, but not an undefeated one nor one without his critics. Belisarius was thus recalled back to the capital, not because Justinian had any grand plans for the general to invade the west, but because Belisarius needed to be reprimanded for his failure! Luckily for him, he was caught up in the Nika Riots, where he was involved in the suppression of the rioters (along with other generals like Mundus and Narses, but again Belisarius was portrayed by Procopius as the most prominent figure), hardly something only a military genius could do. His role in this brutal massacre perhaps brought the general back into favour.
Belisarius was then sent to Africa in 533 and quickly defeated the Vandals under Gelimer. This was indeed impressive, but the Vandal state was clearly ailing by this point, as Gelimer was an usurper and was already facing rebels in Libya and Sardinia. Still, contemporaries thought that Belisarius played a major role in winning the war (he was rewarded a triumph after all), so this is probably the most clear-cut case of Belisarius being a military genius, in the short-term at least. Justinian recalled Belisarius, suspicious of the general's loyalty, and within a year, local Berbers rebelled and mutinies would be common for the next decade. Peace was not restored until 548 and even then the country was supposedly devastated, so perhaps Belisarius' ability extended only to the tactical level. We can also blame this on the corruption and incompetence of the Byzantine administration, but we should not just see territorial conquest as successes by themselves - true greatness comes from creating stability and in maintaining a degree of respect in the long-term.
In 535 Belisarius invaded Italy and scored several quick victories, even securing Ravenna by 540, but Belisarius did not manage to inflict a crushing defeat on the Goths (the war only ended in 554). It is even possible that Belisarius' treacherous seizure of Ravenna had actually motivated Gothic nobles to fight on rather than to make peace. In any case Belisarius was recalled at this point and sent to the east, as the Persians had once again invaded Byzantine territories, but 541 did not see any major military successes - a campaign to Nisibis stalled and Belisarius led his army back to Dara, his main military base, to prepare for a Persian invasion that never materialised, as the Persians withdrew on account of the plague (not because they feared Belisarius, as Procopius claimed). Between 544 and 548 Belisarius was back in Italy, but he was now contending with a charismatic Gothic king called Totila; there would no longer be any easy victories for Belisarius, though another interpretation might be that he simply wasn't given enough resources to fight the war properly. The war was instead won by the eunuch Narses, who led a powerful well-supplied army into Italy in 551. As Procopius had actively portrayed Totila as a heroic figure, almost a protagonist, in his final book, I think a better question is why the tragic yet evidently very capable Totila is as obscure as he is.
Belisarius would not return to prominence until 559, when he raised a temporary force to defend Constantinople against Kutrigur raiders threatening the city - Belisarius by this point had been implicated in several conspiracies against Justinian and had retired from the military. This was a great victory for the Romans , but it was also symptomatic of the crisis facing the government in the late 550s, as their military situation was so precarious to the extent that they had no regular forces or generals available to defend Constantinople, instead needing to rely on a retired general and volunteers to save the day. This is I think a more potent example of Belisarius' ability, rather than his seemingly more dramatic conquests earlier.
To sum up, at a strategic level, Belisarius was not able to secure the loyalties of the locals nor win miraculous victories when he did not have a material/political advantage. He also allegedly had a weak personality, being rather naive and trusting of his adulterous wife, if we believe the scandalous tales spread by Procopius in his Secret History. Unfortunately, Procopius is our main source for this period, so the image we get is rather schizophrenic, that of a young and successful general plagued by a whole host of personal issues. In reality, Belisarius was probably much more mundane, which for me makes him all the more interesting to study. He was just another man in a turbulent age, driven by ambition (and luck) to the forefront of Justinian's wars, only to fall from grace when the mercurial emperor grew suspicious. It does not help that this entire period is relatively understudied, at least amongst the general public - most people can name a few major figures from Greek or Roman history, but who can name emperors or generals from late Roman/'Byzantine' history apart from Justinian and Belisarius?
I'm wondering if there is a particular basis for considering him 'obscure' that you're using which I can test against? Your other comment below that suggests he's fallen out of public consciousness is something pretty subjective that I can't really offer you information about.
We have a lot of material about him, and he added on 40-50% to the Empire during his lifetime. Unfortunately, he did a lot of his work during a time when Rome had lost a great deal of respect and foothold, and ultimately many of his conquests, which were reclaiming previously lost territory, just rubber-banded right back into enemy hands after he left. I believe he captured and lost Rome a total of three times? He doubtlessly had both success and a great career, but I think his effort was overshadowed by the rapidly deteriorating conditions in the West.