Agree with DarthCaedus66, it is not Muspellheim but just Muspell. And Nidavellir is known as well as Svartalfheim, both names are possible so both answers should be recognised as right.
It varies in different texts of the mythologies. Muspelheim tends to be the more common name, but Muspell should also be valid.
In addition, the original texts had Nidavellir and Svartalfheim as separate realms, but these were combined into one in later texts. This is possibly because earlier texts didn't mention Helheim/Hel, which it is speculated was added cause of Christian influences on the religion with their own concept of Hell. So in later texts Hel ends up being one of the nine realms, so Nidavellir and Svartalfheim were combined into one.
while most is true there, i believe anglo saxons made the word hel which christianity later took and used to rename their underworld to hell when it was previously gehenna
Muspelheim is not wrong though. In Old Norse, it's Muspellsheimr or Muspell. Both are widely used and accepted.
The name realms are believed to change after Snori's version (Prose Edda), where Hel/Helheim is added. Before that, Nidavellir and Svartalheim are different realms.
In addition, the original texts had Nidavellir and Svartalfheim as separate realms, but these were combined into one in later texts. This is possibly because earlier texts didn't mention Helheim/Hel, which it is speculated was added cause of Christian influences on the religion with their own concept of Hell. So in later texts Hel ends up being one of the nine realms, so Nidavellir and Svartalfheim were combined into one.
The name realms are believed to change after Snori's version (Prose Edda), where Hel/Helheim is added. Before that, Nidavellir and Svartalheim are different realms.