There’s nothing preventing you from migrating your server but keep the original one running (well… restarting it after you completed your migration). The only downside might be that you need to ensure both devices have a separate machine identifier to avoid “collisions”.
The migration procedure will depend on the OS on your Synology:
- With DSM 6, there’s an established migration documentation → Synology FAQ (DSM 5 & 6) - Questions, Answers, and a few How-To's - #24 by ChuckPa
- With DSM 7 this appears to be a bit more complicated (and work in progress).