NOTE: Not really an answer, but more like bits and pieces of information. I'm unable to find the name, nor a tutorial/solution for it.
On websites like eBay, Amazon, and AliExpress it doesn't really have a name, only a description of tags as they do a lot with puzzles auctions (i.e. Wooden Ball Maze Puzzle Lock Burr Brain Teaser IQ Intelligence Toy or 3D Brain Teaser Wooden Ball Maze Puzzle Board Game Educational Toy for Kids and Adults).. I'm sure it has a name, but I'm unable to find it.
It's produced in China for sure, but I'm not sure under what name or by what producer. It's basically an unbadgedunbandaged version of the Motyl Butterfly puzzle. On the Motyl Butterfly, balls are joined together as pairs, and it has three colors instead of two (here a video which shows it a bit more). The Motyl Butterfly puzzle was produced by Clever Toys, a Czech puzzle manufacturer, in 2005. A solution for the Motyl Butterfly puzzle can be found on Jaapsch' puzzles page.
Your puzzle is definitely easier to solve, since all balls are loose.
The solved state should have two red balls and two white balls at the center:
I don't have the puzzle myself, but looking at it, the solve should be rather trivial. If you put all the balls in one side one at a time (using the other ring to position the next ball), you only have to solve the center four piecesballs in the end.