Depends on what 'logo' you speak of.... Some do. But the traditional 'Steal Your Face' logo (skull with lightning bolt) does not
Another Answer:
The stealie (steal your face) was in reference to a band member's relative stealing millions from the band. They wrote a song about it called "He's gone" There is a reference in the lyrics "Steal your face right off your head" That's where the stealie comes from. There is no specific logo of the Grateful Dead that spells out their name but there are some really cool designs out there on shirts and posters that show their name in a really cool artsy way.
~ the "american beauty" logo With the artists ( Stanley Mouse and Alton Kelley ) not having any intention to have it appear as something else. American Reality. That is the only thing that comes to mind when asking about an ambigram.
The classic logo SYF was done by Bob Thomas and Owsley Stanley AKA Bear. That logo actually intended to have a type of ambigram and spell out grateful dead in the circle with lettering as you look at it from a distance. It was never done though. That idea was given to the main artist Bob from Bear when creating the design in 1969. The song he's gone was written by Robert Hunter first tiime played in 1971, but the SYF logo actually has nothing at all to do with Mickey's father Lenny Hart, the bands manager at one time.~ TI