Here are some MHA villain name options based on the provided information, categorized for different stylistic approaches:

Menacing & Powerful:

• Pyre-Chain: Combines the burning aspect with the chains. Suggests both destructive power and restraint.
• Ember Tyrant: Evokes a sense of fiery dominance and oppression.
• Cinder Shackle: A more poetic and evocative name, hinting at both burning and binding.
• The Iron Pyromancer: A more descriptive title, emphasizing both the chains and fire abilities.
• Malefic Manipulator: Highlights his manipulative quirk and overall malicious nature.
• Chainbreaker: A paradoxical name, suggesting he might break his own chains or those of others, adding a layer of complexity.

Clever & Intriguing:

• The Puppeteer: A subtle name that hints at his manipulative abilities without being overtly violent.
• The Whispering Flame: Suggests a more insidious approach, manipulating through subtle influence and fire.
• Ashen Covenant: Implies a deal or pact made with fire, adding a mysterious element.
• The Gilded Cage: A metaphorical name suggesting both imprisonment and deceptive allure.

Humorous & Ironic:

• Burn Baby Burn: A simple, memorable, and slightly ironic name.
• Chain Reaction: Plays on the word "chain" and his potential to cause widespread chaos.
• The Friendly Fire: A darkly humorous name that contrasts his friendly demeanor with his destructive abilities.

Names Incorporating Specific Elements:

• Kurogane no Honoo (黒鋼の炎): Japanese for "Black Steel Flame," combining the imagery of chains and fire.
• Kettenfeuer (German): Means "Chain Fire," a straightforward and impactful name.

Further Considerations:

To refine the name, consider adding a descriptive epithet or title. For example, "Pyre-Chain, the Puppet Master" or "Ember Tyrant, Lord of the Ashen Covenant." You could also consider adding a surname that reflects his origin or ideology.

Remember to choose a name that best fits the overall tone and style of your story.