The Gremlin logo only changed three times during it's lifetime.
The first one (with a real gremlin) is ommited here as it only appeared on Gremlins 8bit titles.
From 1986 to 1994 the typographic rainbow logo was used.
It took until 1989 for the digital logo to form.
In 1994 Gremlin Graphics was renamed to Gremlin Interactive.
Together with the name change also came a new logo which had to replace the playful rainbow colored 80'ies logo in favour of a clean and modern type logo.
Gremlin Graphics Logo used by Magnetic Fields in their Games
One of the first Gremlin logos. Others from that year exist, but they look rather terrible.