Name the server for the people joining it
A Discord server name shows in a member's server list as an icon with the name on hover, at the top of every channel, and on the invite card people see before they join. That last place matters most: a stranger deciding whether to click Accept reads your name and your icon and little else.
So describe your server the way you would to that stranger. "Study group for second-year nursing students" gets names that tell the right people they are in the right place; "my server" gets nothing useful.
Picking a style
Professional suits communities around a business, a course or a creator's paying members. Catchy and Playful suit friend groups, gaming clans and fan servers, where the name is part of the identity. Descriptive gives plain names that are easy to find when you list the server elsewhere. Mixed gives you some of each, which is the best start if you aren't sure.
Add words you want in the name, such as the game title or your creator name, in the second field. The AI works them into some ideas and explains the choice next to each.
After you pick a name
Rename the server in Server Settings, then match the server icon to it. A server icon is 512 x 512 pixels and shows as a small circle, so a single letter or symbol reads better than a full logo. If you have a server banner, it is 960 x 540 pixels.
Tell members before a big rename. A server they know by one name can look like a different community overnight.