I want to permanently delete one of my ticket fields, however, when I try to delete the field there is an error message that states Could not delete field 'ticket field name'.
You may see this error when attempting to delete a ticket field that is still in use as a condition or action on a trigger. The presence of the field on an active or even inactive trigger will prevent successful deletion. To resolve this issue, locate the trigger where the ticket field is present and either remove the reference to the field or delete the trigger entirely.
For more information, see this article: Managing triggers.