How can one determine the intention of questioners—of whom only their usernames are known on the internet—to decide whether to share the name of the design program with them, especially when the answer is public on social media pages?

If the predominant assumption when using a program or browsing the internet is that most users utilize it improperly for forbidden purposes, then it is not permissible to assist in that. If the matter is ambiguous and cannot be discerned, then it is best to leave what causes doubt. However, if you trust in someone's religiosity and believe they will use it for beneficial purposes, then there is no harm in corresponding with them, and the answer can be sent via private message for fear of others seeing it.