Is it necessary to stop orion services while taking backup of Orion DB?
SQL Server can generally handle a backup of a live system fine. Some DBA's prefer to stop all activity on a DB for whatever reasons they want to come up with, but it is not a requirement and if you think about it there are MANY business critical databases all over the place that are backed up without taking that service offline.
Is there any recommendation from Solarwinds? if you have read it somewhere, please do let me know.
Look at it this way, millions of MSSQL databases are backed up every single night while in service. It would be an extremely unusual circumstance to require the system to stop to perform the DB backups, so they don't go out of their way to say "this database should be treated the same as almost every other database" in the docs, it is assumed that the DBA's are familiar with industry norms.