The car company has said that as of now it does not have any plans for litigation.
Whether or not BMW wants to take any legal action, it may not have any ground to stand on. When Google announced that it was restructuring, the company stated that no products would be built under the Alphabet Inc. name.
This could only be considered a trademark infringement if it caused consumers to confuse the two brands, but without any Alphabet Inc. products that is not likely to happen.
Google and BMW are not the only companies using that name. The U.S. Patent Trademark Office lists 103 trademarks either using the word “alphabet” or a variation of it.