Greta Van Fleet got a thumbs-up on Thursday from the woman whose name it appropriated for the band.

Gretna Van Fleet, the 87-year-old great-grandmother and longtime resident of the quartet's hometown of Frankenmuth, Mich., attended the second of three sold-out shows Wednesday night at the Fillmore Detroit, checking the group out for the first time in five years. With seating and transportation arranged by the GVF members' families, Van Fleet and her husband Dale, along with a few of her other family members, took in the show and met up briefly with the band side stage before the show.

"They've matured, I'll say that," Van Fleet told Billboard. "It was mostly 'Glad to see you again' and congratulations on their accomplishments and so forth. We had seen the parents in between, but not the boys. I hadn't met the drummer (Danny Wagner) yet, so it was nice to meet him."

As for the show, Van Fleet -- who herself played saxophone and piano in a "dance band" with her three brothers during the late 50s -- said she enjoyed it "as much as I could. It's not really my kind of music, but people enjoy it and the boys did a good job of presenting it."

Van Fleet was born in southern Michigan and moved to Frankenmuth 51 years go, where in addition to raising her children she also worked in the local hospital and as a secretary. It was the grandfather of a previous drummer who sparked the idea for basing the band name on hers.

"They were at breakfast and his grandpa told him that he needed to go cut wood for Gretna Van Fleet," bassist-keyboardist Sam Kiszka recalled. "He heard it thought, 'That's an interesting name.' He brought it to the rest of us and I think it was (frontman) Josh who said, 'Let's drop the n out of Gretna, so it was Greta Van Fleet, and that rolls off the tongue better. I think it's an interesting name because it's different. You don't really know what kind of music is going to be produced by this group. I really like that aspect of the name."

Gretna Van Fleet -- who was named for a character in a book her grandfather read -- is enjoying the notoriety, though she notes that "it's been far more than I expected. I really didn't have anything to do with naming the band or anything. When they told me they were going to do that I kind of laughed it off. When I found out they really did it I thought, 'That won't last long. That's not a name for a band.' But they just kept growing and more people ask me about it and I've been far more involved than I expected.

"But so far it's been fun, and I just wish the boys well and keep doing what they're doing."

GVF is planning to do just that, both on the road (with dates booked into October) and in the studio. After launching two No. 1 Mainstream Rock Songs -- "Highway Tune" and "Safari" song -- from its first two EPs, GVF has finished recording its first full-length album, working with producers Al Sutton and Marlon Young at Rust Belt Studios in suburban Detroit and Blackbird Studios in Nashville. Guitarist Jake Kiszka said the material -- which includes songs that have been around for a while and that GVF has played on stage -- is "similar" to what fans have heard before but definitely shows the growth that's come from the vast amount of playing the group has done during the past year-plus.

"I think there's some maturity on the album that you can hear, musically," Kiszka says. "We were able to take our time and try new arrangements and new writing techniques. I think we've become a lot more savvy in the studio as well, so a lot of that will translate to the album. It's very energetic and aggressive."

No title or release date has been announced for the album.