Custom named bosses show "Wither" / "Enderdragon" at boss health bar

If you give a boss mob such as an Ender Dragon or a Wither Boss a custom name, the name does not display at the top of the screen above their health bars, instead it just says the default 'Ender Dragon' or 'Wither'.

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Code analysis: https://bugs.mojang.com/browse/MC-83571?focusedCommentId=294688&page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel#comment-294688