The highlighted part of the sentence is called a/an Professor Plum, who had been to the mansion before, expertly navigated the maze of rooms and corridors to quickly reach the conservatory

The highlighted part of the sentence is called a/an Professor Plum, who had been to the mansion before, expertly navigated the maze of rooms andcorridors to quickly reach the conservatory

I think this is what you are wanting to know. You would use a not an If the word/name (Professor Plum) would have been something starting with a vowel instead, you would use an

Is this what you were asking?