Bennett is a variation on Benedict, and means blessed. It's been on a slow and steady rise from its low point in 1975 (when it was the 943rd most popular baby name)—it's currently about to break the top 200 names in the country.
Armistead is an intriguing choice. It's a surname name that means "hermit's place," and hasn't ever been in the top 1000 in the U.S. Early in her career, Laura Linney starred in a mini-series based on author Armistead Maupin's Tales of the City—which may have been the inspiration behind her name choice.
Overall, it's a really classic, weighty name—it feels like the name of a classic author or playwright.
Image: Laura Linney by Jaguar PS/Shutterstock.com