Brutus is a Roman name which means "heavy" in Latin. Famous people with the name include Lucius Junius Brutus, the founder of the Roman Republic, and Marcus Junius Brutus, who helped kill Julius Caesar (Behind the Name).
Scrimgeour is a Scottish clan name. It probably originated from a nickname meaning "skirmisher" (a version of escrimeur, which is French for "swordsman") (Internet Surname Database), a fitting name for a bat-wielding Quidditch Beater.
From the Web
WizardingWorld.com (Pottermore) features:
- Quidditch Through the Ages
- A Blaggers guide to Quidditch
- How to survive a Quidditch match
- Which Quidditch position would be right for you?
Harry Potter Wiki: Brutus Scrimgeour