By adding an external tool to your course in Blackboard, you will give the new FeedbackFruits assignment a name as displayed here: 

FeedbackFruits synchronizes this name one time. As you can see below in the top left corner, the name given in Blackboard is used as the title of the assignment in FeedbackFruits. 

After setting up your assignment, if you change the title within the FeedbackFruits assignment, you need to also manually change the title of the assignment in your LMS. Otherwise, the title displayed in FeedbackFruits is different from the title displayed to colleagues and students in Blackboard. This could especially create confusion when sending back a deadline to your LMS.  

With the tools enabled through LTI, the above accounts for every LMS. 

...synchronization happens the other way around. Using LTI content item, you will first set up the FeedbackFruits assignment. By doing this, you are asked to give the assignment a name within FeedbackFruits, as displayed in the screenshot below. In this case, too, the title is synchronized one time with Canvas. If you change the title afterwards in either Canvas or FeedbackFruits, this won't synchronize automatically and you have to manually update the title.
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In Moodle
​When you first create an assignment in Moodle with FeedbackFruits as external tool, the title will be automatically synchronized. This will happen just one time. However, if you have already created a FeedbackFruits assignment in Moodle and want to change the name, you will have to do it manually both in your LMS assignment and in the LTI content item, as they won't synchronize automatically. First, you will have to change the name through the 'Edit settings' option in Moodle. 

And afterwards, you can press on the three dots on the right in your FeedbackFruits assignment, and 'Edit'. Then you will be able to manually edit the title for this assignment as well.