The 'O.M. (First Class)' in Professor McGonagall's name stands for 'Order of Merlin, First Class'. This is an award bestowed upon wizards and witches who have achieved great things for the wizarding world. It's the wizarding world's equivalent to the Order of the British Empire, with three different award levels: First Class, Second Class, and Third Class. Professor McGonagall, being a prominent figure in the Harry Potter series, was awarded the First Class for her significant contributions.