Hi, do you add these new records to the DNS of DO droplet or Name.com?
And if you add it to DO droplet, would it conflict with the current DNS in DO, like such?
@ A 11.111.111.11 (the current DNS for the site to work in DO)
mail.davelukas.net A 22.222.222.22 (old site ip)
Would having 2 simultaneous A records be a problem, no?
It depends on what your domain's nameservers are set to. If they are set to ns1-3.digitalocean.com, you need to use DO's control panel.
Having multiple A records shouldn't be a problem, as long as they are of different names. So, the new A record needs to be called "mail" so that your main website doesn't conflict with it and because the MX records points to the DNS record that is called "mail".