I am planning a world of different animals that live in Siberia and think about names I don’t there names to be Russian names how do I go about thinking of their names?
Naming things is one of my biggests weakness. The best advice I can give is: don't let a lack of names stop you from writing. Use placeholders if you're stuck. Call the bear Dave and come back to it later.
That said, for my current project I'm using a technique that involves combinining two existing words in a language of your choice to create a name. So, for example, you might take a word like Rosa (Rose) and blend it with another word like Spina (Thorn) to make something like Rospina. I like to pick words which relate to the characters in some way but you can open a dictorionary to a random page or use an online word generator if you're stuck. You can also use this technique to combine two existing names or a name and a word. I've seen some people combine words from two different languages to come up with something unique. If you use this technique, I would highly reccomend you look up any name you come up with to make sure it doesn't have any negative assositions. Portmanteau name generators may also be helpful if you're interested in trying this.
As you're naming animals, I think nature names and/or names based on (physical and non-physical) characteristics could work quite well. Think names like Ravenpaw (Warrior Cats), Hazel (Waterhsip Down), or Fearless (Braveland). It works best if they're naking themselves either after things that could be found in their enviroemnt or how they'd think of each other. Both of these can help make them feel a little less human. Different species could also have different naming conventions, e.g. an animal with good vision might focus more on visual elements when naming their offspring. Name generators could be helpful if you want to go this route. You can also combine this with the portmanteau technique above. If you find this one a little odd, just imagine that the animals are speaking another language and your translating it as closely as you can into English (or whatever language you're writing in).
Another ooptions is to use vulgarlang to generate a new conlang and use the name generator button that comes with that. Russion is one of the options under word structure, if you want to generate a language that sounds like Russian but isn't.
There's no law saying you can't give them human name either. Redwall uses Matthias and Martin and I don't think there's anything wrong with that. If you don't want to use Russian or English, there's other languages spoken currently and historically in Siberia you can borrow from if you'd like to use human names.