No, you don’t need to learn a dead language in order to practice yoga. Many yoga instructors refer to postures in their Sanskrit name. Of course, each of these postures also has an English translation, but many yoga instructors (and yogis) prefer to use the Sanskrit name (though, to my knowledge they don’t speak Sanskrit in other capacity). Some people (myself included), thinks this comes across as pretentious and unnecessary, and for this reason I don’t use any Sanskrit in my instruction.
There’s absolutely no need to learn Sanskrit to practice the postures with proper alignment - and despite what some yoga instructors may tell you, there is absolutely no difference in the benefit received if you refer to the pose in its English translation instead of using the Sanskrit term.
If you have an instructor who uses Sanskrit and it annoys you significantly, you can always find another yoga instructor. Again, there are literally thousands of yoga instructors out there, and there’s bound to be one with whom you can relate