How to verify the obtained SNR of the noisy signal after adding noise?
Here is a common/straight-forward way using the discrete time domain samples. If you have the noise free signal, $x[n]$, and you created a noise signal, $w[n]$, then you can calculate the SNR by using the formula:
$$\hat{\text{SNR}}=\frac{\sum_n |x[n]|^2}{\sum_n |w[n]|^2}$$
Edit
An unstated assumption above is that $\mathbb{E}\big[x[n]\big]=\mathbb{E}\big[w[n] \big]=0$. In general, you'd use the variance not the sum of squared values, as to take care the possible non-zero means:
$$\hat{\text{SNR}}=\frac{\text{var}(x[n])}{\text{var}(w[n])}$$