Alastor (People just call him Mad-Eye)
Professor Sprout's first name is Pomona
Quirinus.
Horace
The full name is Sybille Trelawney.
James
The plural for Moody is the Moodys.
Professor Smith's first name is not provided in the question.
Elmo
Professor Sprout's first name is Pomona
Professor Layton and the Curious Village.
Professor Fiendish's first name in the "Murderous Maths" series is Norman.
When a professor signs their email with only their first name, it is appropriate to address them using their first name in your response.
Quirinus.
Horace
The full name is Sybille Trelawney.
Filius
Minerva