If you want to host your wordpress site on your Synology DSM NAS, you will only need an DNS server where you can register your Synology DDNS name and open your router on port 80 and 443.

Basically, I have followed this article https://pfbarrett.uk/transferring-a-wordpress-site-to-a-synology-nas/ to install WordPress version 5.4.2.

When entering the database access in the ‘Famous 5 minutes install’, I had first to go in the ‘Web Station’->’PHP Setting’, select your PHP profile, click edit and check ‘mysqli’ and use localhost:/run/mysqld/mysqld10.sock.

I also checked ‘curl’ as without that extension, I was not able to download new plugin versions (no available transport).

Last, I sshed my synology, changed to directory /web and change the owner and group recusively to ‘http’.
sudo chown -R http; chgrp -R http