The answer is almost certainly related to aesthetics rather than any deeper meaning. The logo has been portrayed inconsistently throughout the Bond franchise, with the octopus starting out as a quadropus, then becoming a proper octopus, and most recently, being rendered a septopus. Many Bond fans argue that the original Dr. No/From Russia With Love design, with four "legs", was never supposed to be an octopus, and was intended to represent a ghost; according to these fans, the franchise mistakenly turned the ghost into an octopus in Thunderball. The image itself lends some credence to the idea that the original logo was a skull with ghostly trails below, but I haven't been able to find any canonical references to support it.
Note that in the new design:
The octopus is more stylized than was the case in the previous logo, more sinister, less cartoonish, and less obvious.
The octopus is drawn in such a way that it also resembles an actual spectre, or ghost.
The new design is sleeker, more modern, and combines the symmetry of the previous, eight-legged design, with the menace of the original design, which looked as much like a skull as it did a cephalopod.
Additional motivation to change the logo was introduced by the MCU, and its SPECTRE analogue, HYDRA:
SPECTRE left, HYDRA right
The film's producers would certainly want to avoid any confusion between the two logos.
Or perhaps the latest incarnation of SPECTRE is fond of the so called "Seven Armed Octopus", which gets its name from the fact that the specialized tentacle used in reproduction is kept hidden from sight in males of this species.