does anyone know if you can set the task name column in a task list to be a drop down list of values. I have a predefined list of tasks that I would like a user to select rather than input themselves. The task name seems to be a system owned column which means I am not able to change the column settings.
No, you cannot change that column, but there's no reason why you couldn't create your own new column, named something like "task type" that is a choice or lookup column. Then add that column to your various views and/or use as a "group by" column.
If you create it as a site column first, then add that existing site column to your task list, SharePoint will also automatically create an indexed managed search property so you can key searches and highlighted content off it as well.