They didn't call it that. They called it RDS-202 or one of a few other RDS designations.

It isn't clear when people started calling it the "Tsar Bomba" but it seems to be a post-Cold War thing. The US called it "the 100 megaton bomb" at the time. One newspaper tried to coin the term "K-bomb" (for Khrushchev) but it didn't catch on. Sometimes it was called the "monster bomb" but this was pretty rare.

This Google Ngram paints a little bit of the picture. It's a little misleading because the total sample size is very low, so even dating mistakes look significant (e.g. some of the very early ones), but you can see that "Tsar Bomba" just comes out of apparently nowhere around 2000 or so. Even in sources from the mid-1990s they don't call it that (e.g. Peter Kuran's Trinity and Beyond, which is responsible for putting footage of its detonation into the public domain, calls it the "Monster Bomb"). I still haven't traced who coined "Tsar Bomba."

Source: I have been researching the bomb in question for some time and am writing an article about the US government responses to its creation and detonation.

Update: I poked around a little more through my resources on the topic and tried to find the earliest use of that name that I could. The earliest one is from an article in the history journal IEEE Spectrum from 1994, where it is mentioned in a caption that went along with a photo of the casing when a Russian museum on nuclear weapons became open to the public. The author of the article is an Alexander Kalinin, a Russian engineer/physicist who was at the time working in the United States at the Monterey Institute for International Studies. Today he apparently lives in Korea and works as part of UMUC Asia's faculty, but I could find no contact information for him. I would love to ask him where he first heard the phrase used — I wonder if it it comes from the museum exhibit. Or if he even wrote the caption (authors often do not).