When I read this question I got curious and decided to find the answer. Whilst I'm not a trained historian, I hope my amateur answer will do.

To find the answer, I decided to look in the Dutch newspapers of the time, and I stumbled upon this article in the Telegraaf: https://resolver.kb.nl/resolve?urn=ddd:110550067 .

The newspaper article mentions two sources for the death of Nicholas II:

1. Wolffbureau (Berlin, 20th of July 1918): The former tsar of Russia has been shot on the 16th of July in Jekaterinenburg.
2. Reuters (London, 20th of July 1918): The former tsar of Russia has been shot on the 16th of July. His wife and sons are still alive. The information is based on an official wireless telegram from the government in Moscow.

I'm sure a lot of similar newspaper articles can be found, but I liked this article for the fact that it actually mentions it's sources quite nicely.

The first Dutch publication I can find is in the Leeuwarder courant (20th of July): https://resolver.kb.nl/resolve?urn=ddd:010601333

So to answer your question: the murder on Nicholas II has not been covered up. Instead, the Russian government sent out a wireless telegram, which was then copied into German and English newspapers on the 20th of July.

If anyone is able to actually find the telegram of the government in Moscow or the publications by Reuters or the Wolffbureau, it would be interesting to see in what way the death was first communicated.