What is the name of the function which results from sampling a sigmoid?

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It is not just two Gaussian distributions. I would hope that it is defined and has a name, but I can't find it. I would love to know more about it (parametric formula, how to extract the parameters given a sample...).

Example Shape resulting of uniform sampling a sigmoid

PS: Not particularly of interest, I think, but the above was obtained using this formula:

sample_normal + 2 / (1 + exp(-0.5*(sample_uniform*20 - 10)))

... where 'sample_normal' is a sample from a normal distribution(mu=1, sd=0.1, N=500), and 'sample_uniform' is just 500 random numbers from 0 to 1.

Thank you in advance for your time and help!