What is the ruling on accepting offers to write names in Arabic calligraphy for non-Arabs for the purpose of using them as a signboard or on their private website, with the fear that they might be used later for tattooing?

You were right to abandon assisting in forbidden acts, and Allah will compensate you with something better than the illusory profits you missed. As it is stated in the Hadith: "You will not abandon anything for the sake of Allah, the Mighty and Majestic, but Allah will replace it with something better for you than it."

As for what you do not know is used in forbidden acts, the basic principle is that it is permissible to work on it, unless it is highly probable that its user will employ it in forbidden acts; in that case, you must avoid dealing with them.