Can You Get Banned in ESO Just For Having a Lore Friendly Character Name?

Let's be honest - it isn't very uncommon for players in the Elder Scrolls Online to have lore friendly names, such as the surname Telvanni. People who are interested in roleplaying are especially likely to name their characters in this way. 

It's also not uncommon for people to name their characters after an existing NPC or lore character, either in ESO or another Elder Scrolls game, such as Skyrim. 

However over the last few days there has been a storm of confusion and controversy surrounding this issue, with players reportedly getting banned from the game for having names like this. This has left some players worried for their characters, others just angry about the rumored bans, and Zenimax employees scrambling to offer clarification. 

So what exactly is all of this about, and do you need to be worried?

Would naming your ESO character after Vivec result in a ban?

Banned for Being a Telvanni?

So do I need to Worry about my ESO character?