RemcoGerlich's answer is excellent: the Lasker-Pelikan and the Svechnikov are basically the same variation; it is defined by 5...e5 but the line until 8...b5 is the main continuation afterwards and the resulting position where White can choose between 9.Bxf6 and 9.Nd5 can be considered as its real tabyia. The name "Lasker-Pelikan" is outdated, almost obsolete, and nowadays "Svechnikov" is the way to call that variation.
To complement the historical evolution, the variation was known as the "Lasker-Pelikan", or just the "Pelikan" until the beginning of the 70's, when it was considered dubious and was not popular at all. Then youngsters like Svechnikov, Timoshchenko and Vladimirov gave the line a boost, but because they were no famous grandmasters (yet!) but just some obscure teenagers, Russian theoreticians named the line from the city they were coming from, Tcheliabinsk - for about 10 years 5...e5 became "the Tcheliabinsk variation" (or even sometimes "the Tcheliabinsk-Novossibirsk variation" !).
In the eighties, Svechnikov became a strong grandmaster, kept being successful with his pet line and wrote a good reference book about it, so more and more people referred to the line as "the Svechnikov Sicilian" and that is the standard name ever since. Yakovich's, Rogozenko's, Kotronias' and Lakdawala's books about the variation all have the name "Svechnikov" in their titles.
Evgenny Svechnikov's own book about the line is actually entitled "The Sicilian Pelikan". I think it was published in 1986 or 1987 in the USSR, what is sure is that the English translation went out in 1989. This title is a display of modesty by the author, since the names "Svechnikov", "Svechnikov-Vladimirov", and "Tcheliabinsk" were already much more in vogue than "Pelikan" in the eighties.
Another early expert from the city of Chelyabinsk who contributed a lot to the develoment of this opening, Gennady Timoshchenko, just published his own book about the variation, entitled "Sicilian Defence - the Chelyabinsk Variation".
Its "Part I The History of the Variation and Its Development" includes a chapter "About the Name of the Variation" that would be very interesting in regard to this question. Especially if we consider the author's contempt for Svechnikov's analyses !