Is it permissible, Islamically, for a man to marry a second time without informing the ma’dhoun (marriage officiant) that he is already married, and [to tell him] that this wife is his first, with the intention of concealing the news of his new marriage from his first wife?

What the husband did by marrying this woman of ill repute is something that should not be done. Rather, one should choose a wife who is religious, well-mannered, and of good reputation, in obedience to the Prophet's (peace be upon him) saying: "A woman is married for four things: for her wealth, for her lineage, for her beauty, and for her religion. So, succeed with the religious woman, and may your hands be dusted (i.e., may you prosper)."

As for his lying to the marriage official that he was not married, this is not permissible, for lying is forbidden. However, his marriage is valid if it was conducted with the permission of her guardian, the presence of two just witnesses, and with offer and acceptance.