IMHO, there are a couple of reasons why someone decides to change their brand name:
1) They might have discovered they do not own the rights to that name in a specific market that they wish to enter. A trademark is not worldwide. Some countries honor US trademarks, and some do not and make you register your brand in their country. In Australia, Burger King restaurants are called Hungry Jacks because the Burger King was unavailable. What is odd is that in this situation, most companies would change the name only in the new country (as Burger King did), not everywhere.
2) They might have discovered they do not own the rights to that name in a major market they are ALREADY selling in. This is much worse than #1, and can result in major lawsuits and big settlements.
3) They might be trying to introduce a new line under a different brand name. This allows them to move laterally in the market to try to capture a different segment that might not buy their primary line. This might be a higher-end line, a lower-end line, or a completely different style or category of product. It might also allow the manufacturer to use a different distribution channel that is not covered by their existing Sales contracts. This allows them to avoid being accused of creating competition by their existing resellers. In this last case, you would normally want to have clear separation between the names - you wouldn't just change one letter.
4) They might be creating a different brand and legal entity in order to end a warranty practice that existed with the old brand. For example, if you had a lifetime warranty on a product, and you didn't want to produce any more products with a lifetime warranty, then you could change the brand name, and the new products with the different name would now have a different warranty. This makes it much easier to draw a line in the sand and know that no new products are going to be produced that require support forever. This make the accountants in the Finance department very, very happy...
5) Some wank from the Marketing department thinks he is the next Don Draper
and makes all kind of promises about how this change will boost sales by XX% and they will all be richer than Jeff Bezos & Elon Musk combined.
Take your pick...
"The Luggage had a straightforward way of dealing with things between it and its intended destination: it ignored them." -Terry Pratchett