You can’t change the UID of osmc but it can become a member of an additional group.
So, first create a new group using the same GID as on the Synology NAS. I’ll use 1234 in my example.
On osmc, run:
sudo groupadd -g 1234 synology
then add osmc to the synology group:
sudo usermod -a -G synology osmc
Then logoff and logon again. Type groups (or id) to check if you’re in the synology group. You then need to set whatever permissions you want for the group’s access.