Why is the Gray code called a cyclic code?
cyclic
ˈsʌɪklɪk,ˈsɪklɪk/
adjective
1. occurring in cycles; regularly repeated.

You haven't given a reference for the 'cyclic code' terminology but there is certainly a cyclic patter. This is most obvious in an encoder disc.



Figure 1. The cyclic pattern of each bit is clearly visible on this optical absolute encoder disc.

Each bit has a repeating on-off pattern with a 50% mark-space ratio. The bits are arranged so that only one bit changes at a time. This prevents errors on transitions from one code to the adjacent one due to misalignment of sensors, etc.

There's a generic definition about the cyclic nature of the Gray code further down the Wikipedia Gray code article mentioned in altai's answer: "The last entry in Gn differs by only one bit from the first entry. (The code is cyclic.)". That is it can wrap while still maintaining only one-bit change.

It would be possible to generate a Gray-ish code that didn't have this property if, for example, the number of steps was not even or a power of 2. This might be acceptable in a linear encoder which wouldn't need to wrap.