Simple plugin, links with PlaceholderAPI to add the placeholder %bungeeservername_name% which resolves to the name of the Bungee sub-server you're on, as defined in Bungee's config.yml. I couldn't find any plugins that do this already, so here it is.

There are two commands, /servername, and /updateservername. /servername will print the name of the server so you can test if it's working.
/updateservername will re-check the name of the server ASAP. Because it uses BungeeCord messaging channels, the server name can only be updated when there is a player online. If the command is used from the console when nobody is online, it will check the server name next time a player joins.

Because PlaceholderAPI supports getting placeholders for offline players, it's possible that the placeholder could be used when nobody has connected to the server since it started, in which case it will use the last-known value of the server name, stored in the plugin's config.yml

Note: This is an actual plugin due to the need for messaging channels and other things, so it needs to be installed into the plugins folder, not the PAPI expansions folder.

Note: This placeholder is not player-specific, and will not get the server of another player or any such thing.