Nomenclature and bonding of the complexes ions
The bonding of the $N$ end of the thiocyanato group to the Metal centre $\ce{Cr^3+}$ can be explained by both HSAB Theory and Symbiotic effect.According to HSAB Theory, Hard acids prefer to bind with  hard bases, while soft acids prefer to bind with soft bases. Here the metal centre is $\ce{Cr^3+}$, which has $3d^3$ electronic configuration. So,  $\ce{Cr^3+}$ satisfies the criterions for a Hard acid centre, as it has very less no. of $d $ electrons, high positive charge density on it, smaller radius and greater polarisation. So, the metal centre in this complex acts as Hard acid centre. And, now if you consider the properties of a hard base, you will find that $N$ is the harder basic centre, whereas, $S$ is the softer base centre. $N$ has higher electron charge density on it and also smaller in size than $S$ which makes it harder base. Thus, due to the presence of the harder metal acid centre, the ligand tries to bind with the harder basic centre, which in this case is $N$. The attachment of the $N$ site can also be explained by the Symbiotic effect. Observe that, in the complex, you already have two $\ce{NH_3}$ ligands donating through the $N$ site, which actually compells the thiocyanate ligands also to coordinate through the $N$ site, which is the main idea of this effect. Actually, donation through $N$ sites of ammonia makes the metal centre even more hard, and therefore it prefers also the $N$ site of other ligands.  But a remark which is necessary is that the HSAB theory doesn't always predict the correct coordinating site for an ambidentate ligand. If even stronger effects like Competitive $\pi$-Bonding effect start to interfere due to presence of $\pi$-accepting and $\pi$-donating ligands, HSAB theory may not give a correct answer at all. So, in the absence of those effects, HSAB theory  works well.