My model file has a value in the user field of each object that I would like to use as the task name.  (e.g. the panel name for a bunch of precast panels we're sequencing). Is there a way to automate the renaming of tasks? 

You can use Script to automate renaming the tasks.

After the Resources are all assigned to the desired tasks:
1. Select one of the Resources and confirm the exact name of the User Field you wish to use. You can copy the UF name from the Navigator>User Fields list if needed
2. Select the tasks that you would like to rename
3. From the Project Controls ribbon, open the Synchro Script window
4. Enter the following script into the text box:
TASK (SELECTED) SET_PROPERTY (NAME, RESOURCE.UFV ("User Field Name"))
and replace "User Field Name" with the exact name of the User Field you wish to use. 
5. Press Preview to make sure that the correct tasks and User Field Values are found
The Object column will show the selected Tasks with their original name and the Argument column will show the User Field value that is to be used for the new Task name
6. If satisfied with the Preview, press Run, then Close to return to the Task List