What are laws called that are aimed at specific people?

Such laws are generally called "private bills" or "special laws." If the private bill is meant to punish a specific person or group, it is more precisely called a bill of attainder.

Private bills are rarely used today because much of what they once did is now accomplished through administrative agencies. However, they still appear in matters of Immigration and other areas.

Private bills are sometimes restricted by state constitutions. Bills of attainder are prohibited by the US Constitution.