Please following steps:
1.Add column to your list. For example, add [Status] (Choice column) and set default value is Pending.
2.In order to avoid endless loops, you can set conditions: update item when [Status] is Pending, and change [Status] to Completed. Then it will jump out of the next cycle.
Add Condition action to the Microsoft Flow:
- Manager's Name Claims is equal to null
- Manager's Name Claims is not equal Display Name
======================= Updated Answer ========================
In My Testing:
1.Create new item:
Updated Answer ========================
Get user profile (V2) User (UPN): Engineer's Name Email
Condition: Manager's Name DisplayName
is not equal to Display Name
The Flow will be triggered twice, because as long as the value of the item is modified, the flow will be triggered. However, if the Manager's Name Displayname is equal to the Get manager Display name, the item will not be updated and break out of the loop.