Who is “Your Opponent”?

Solution 1:

Along with the two forums you linked, this Battle Net forum discussed this as well. While it doesn't contain any information directly from Blizzard on this, a user gathered that this is more than likely due to a connection blip from the server.

From what I've gathered there is only one very small window that the Hearthstone client sends the opponent information to your game client; that being right at the very start of the connection to the match. If you glitch and your connection hiccups, that information can be lost, and your client doesn't know your opponent name and rank. (Though the server still knows that information.)

Since the server still contains the information of who you faced, you were able to look at the history and see the name of the player you battled against.

Solution 2:

While the answer given by Wondercricket was true when posted, there's actually another reason why this is happening more frequently now. In October 2017 Blizzard added "Appear Offline" mode for players - partly to counter queue sniping.

When you choose to appear offline, opponents will now only see "Your Opponent" as their opponent's name.