In canon, this is a complicated question. Officially, Palpatine's Vizier Mas Amedda is the new Emperor, but he has no real power in the position:
[E]verything else is out of [Amedda's] hands. Everything but minor administrative details.
It is lonely being the head of a dying Empire.
He is a figurehead. Or worse than one. They don't even trot him out for appearances.
Aftermath: Life Debt Chapter 10
It's not immediately clear who actually does have any power after Palpatine's death; it's clear that there's a great deal of squabbling amongst factions, and Grand Admiral Rae Sloane is said to control the Imperial Navy, which gives her a great deal of influence:
"Grand Admiral Sloane," [Amedda] says.
She stands up.
Here, before him, is the leader of one of those Imperial fragments — a rather considerable one. Perhaps the fragment of note. She controls what remains of the Imperial Navy, and their navy is dominant, so it is clear that whoever controls the navy controls the Empire. More or less. Still, it leaves her without the bulk of the ground forces, but rumor already has it that she's begun to bridge that gap and complete the deficit in her military presence.
Aftermath: Life Debt Chapter 10
The most influential is presumably Gallius Rax, an Imperial Fleet Admiral who assembles a Shadow Council to rule what remains of the Empire; Sloane herself, an astute political mind, notes his influence (emphasis mine):
Sloane bristles at being interrupted. Hux1 undercuts her because he thinks she's not important. It is vital she make a show of countermanding that — honestly, her greatest desire right now is to slam her fork through the back of his hand and chastise him for the intrusion. But that would defy Rax, and she's aware suddenly of the keen and delicate balance of power.
Aftermath: Life Debt Chapter 12
Rax eventually sets Sloane up as a puppet leader, with himself pulling her strings:
Sloane narrows her eyes. "You're pulling strings, Admiral. I don't know what they're connected to or why you're pulling them. I don't even know who you are or where you come from. You are little more than a shadow — and yet you lead the Empire."
"Secretly. You're the grand admiral here, I'll remind you."
Aftermath: Life Debt Chapter 18
And, after Sloane disappears, Rax himself assumes (theoretically temporary) control of the remaining Empire, though under a different title:
"Are you claiming the mantle of Emperor?" Borrum asks.
Rax hms. "I think not. I am not worthy."
"Grand Admiral, then."
"No. I am far too humble for such mighty titles. As I am the adviser to this group and to the Empire at large, I shall take for myself the title of Counselor to the Empire, serving as an interstitial leader only until Grand Admiral Sloane returns to us."
Aftermath: Life Debt Chapter 40
Rax's Empire would eventually disintegrate, and the most successful of the resultant factions would become the First Order, under the command of Supreme Leader Snoke.
1 No, not that one