I am very new to Nintex but we have a case where users are customizing the list column names and the workflows are breaking. Is there a way to create a nice "display column name" without breaking the underlying workflow?
It sounds like the workflow is attempting to reference a list column and the names are not matching. This should not happen as the workflow will hold the reference of the column and update any changes.
Are you able to see the history and see exactly where the failure is? Might be able to pinpoint the exact cause better.
It's a very good question to answer in the planning and governance documents and a topic to educate your users about.
Any change to a list's schema (including but not limited to column settings) while the workflow attempts to update an item will definitely break the workflow instance. At the same time, publishing another version of the workflow that modifies the schema as well will also cause trouble for users who opened their edit forms just before the publish operation - they are very likely to lose their changes and see an invitation to refresh the page and try again.
As for pending and new workflow instances, this may vary depending on the actions used in the workflow template, let's wait for an official response from Nintex (CC Frank Field).
I just started a new position and this is all very new to me so I don't have access to the system to check. According to my team, there are cases where the workflow does not automatically start and they say it is because users have made changes to field names and the workflow cannot find the field it needs.
In doing some research on SharePoint workflows, it seems like a change to the display name does not affect the underlying static name so I didn't really understand how this would break the work flow.
Ask your team to search the ULS logs of the SharePoint servers for the ID of the terminated instance or for (Legacy) Workflow Infrastructure messages around the time when problematic items were added or changed. That might give some clues as to the reason of failing starts.
Sometimes workflows fail to even start trying when an error occurs before they have the chance to respond to the asynchronous events such as "item added/updated". One of the notorious cases is when users submit items with attachments and one of those is rejected due to unsupported characters in the filename or an unsupported extension or a timeout expires during the upload.
Changing field names rings a bell for me, reminding of a case when a workflow template was exported from dev and imported to another environment and a few backing fields were manually created with different names, but the list designer didn't confess to that upfront
There are many possible causes, but the change of column Display names is really not a Problem. The first potential Problem, namely "event item added/updated", has already been mentioned by Alexey Krasheninnikov. If that is the Problem you can try to set the Action "Wait for item update" at the beginning of the workflow (for example with configuartion "Wait for Created By to be not empty". Of course you can also select a column created by you or your Team. This problem occurs very often by Document Libraries -Workflows that automatically start.
The next frequently occurring problem happens when a workflow is running under the system account, what in most (read never) cases should happen. If the workflow starts automatically, for example, when an email is received, you can put all your actions in an "Action set" and then check the checkbox to "Run as Workflows´owner" (Configure Action->Common). Off course, must the workflow owner have sufficient privileges.
If you configure the action set to run as workflow owner, make sure that you publish the workflow as a non-expiring system service account. Otherwise, when you make your next career move and you account's permissions are changed, your previous team might have a few unpleasant words to remember you with.