There are few more powerful beings in the Marvel Universe than claimed the Dark Dimension as his own after being exiled from his home reality. However, while Dormammu's flaming head may be iconic, he does have another face that will surprise fans of his MCU portrayal.
Dormammu is a member of the Faltine, a species of energy-beings composed of pure magic and shaped like fiery spiders. Faltine are unusual in giving 'birth' to exact duplicates referred to as Scions, who likewise feed on magical energy and serve to increase the status of their parent (or 'Genitor') in Faltine society. However, Dormammu and his sister Umar broke from this pattern, being unique beings unlike their Genitor Sinifer. So different were Dormammu and Umar from the rest of their people that they became obsessed with absorbing matter rather than energy - a goal which drove them to want physical forms and quickly got them driven out of their home.
In Doctor Strange: Sorcerer Supreme #22's 'The Book of Vishanti: Legends and Lore of the Dark Dimension' - by Roy Thomas, R.J.M. Lofficier, Lee Weeks, Jean Simek, and Nel Yomtov - fans learn the history of Dormammu and his sister, and how they journeyed to the Dark Dimension as part of their quest to consume even more matter. To do so, they adopted human forms comparable to the Dark Dimension's native life forms, choosing the aspects of humans in their prime. However, once they had seized control of the Dark Dimension, Dormammu chose to merge his Faltine and 'human' forms, leaving him with a human body and a flaming Faltine head (Umar has generally chosen to appear human ever since.)
Looking at Dormammu's history, it's clear that his flaming head is indeed his natural and current form. While Dormammu has worn a human face in the past, it was one he shaped from matter, and could theoretically be anything he chose. However, there is some evidence to suggest that he may revert to this face if stripped of his powers. Recent issues of Strange have seen Clea - Dormammu's niece - manifest Faltine flames at the height of her power. Likewise, Ultimatum: Fantastic Four Requiem (Joe Pokaski, Robert Atkins) sees Dormammu revert to a human form when his flames are extinguished, though this story takes place in Marvel's separate Ultimate Comics continuity.
Dormammu ceased to be a true Faltine when he first absorbed matter, and has spent a long time in his pseudo-human form. Given how modern comics treat other, similar characters, it's possible that if he's deprived of enough energy, his constructed human face may be waiting beneath the flames, simply due to the fact that Dormammu originally re-created his Faltine energy head on top of his "permanent" human form. However, in every way that matters, Dormammu's 'true face' is indeed his flaming head - a fitting form for a villain so vile he makes even Doctor Strange shudder.
