How Veeam to handle truncate logs action?
That depends on what truncation option
What method does Veeam to use?
Not sure what you mean, could you please elaborate?
Once truncated logs to Veeam backup, are these logs will Increment?
If you are asking if the copies of logs inside the backup will increment, then the answer is "No". Logs are stored as a separate set of files thus each new log backup session will create a new log backup file in the repository.
Any other permission setup in SQL database?
Please see this article
(the very bottom of it).