No, entropy is the same in all reference frames. Entropy is the logarithm of the number of accessible states and hence is a pure, dimensionless number. A pure number is a 0th-order tensor. (A vector is a 1st-order tensor.) 0th-order tensors transform into themselves in going from one reference frame to another. (Likewise, if there are 5 apples in one reference frame, there are 5 apples in all reference frames. 5 is a pure number. Of course, the mass, velocity, etc., of the apples depends on reference frame, but not the number of apples.)