Is it recommended for his family to name his son on the basis of that which is connected to astrology and soothsaying?
There is nothing wrong with naming children on the basis of events or times that coincide with their birth. There are people who called their daughters Marwah or Safa because news of the wife's pregnancy reached them in the sanctuary in Makkah, or because they were on the hills of al-Safa and al-Marwah. Some of them called their son Badr because his birth coincided with the Battle of Badr. Some of them called their son Ramadan or Sha’baan because they were born in one of these two months. There is nothing wrong with any of these things, because they are not contrary to sharee’ah.
Similarly, there is nothing wrong with the father giving all his children names that start with the letter meem or alif, as some of them do. The matter is broad in scope.
What matters in all these choices is that this should have no connection to soothsaying or any other belief that is contrary to sharee’ah. The one who believes that if he gives his son or daughter names such as we have mentioned above, this will bring his child good luck, or that he will attain a high position or wealth, is forbidden to use this name, because beliefs such as this have no basis in Islam; rather they are myths that stem from superstition and soothsaying.
Based on that, if you discover the truth of the matter and that your husband's family believe these myths about naming children, then you should not agree to what they want, even if that leads to them resenting you, because these traditions and customs that are contrary to sharee’ah must be resisted and opposed until the people turn away from them.
Before that, you have to explain to them, kindly and gently, the error of what they believe and what they want to do, and that it has nothing to do with the happiness of the child.
If they respond, then praise be to Allaah. Otherwise you have no choice but to go against their wishes and choose a good name for your son.
If you are wise and you go along with what they want, then who will put an end to this chain of myths?
We ask Allaah to guide you all to the right path.
And Allaah knows best.