Agreed, very weird to have two names.
They should just go ahead and name the product "Hellmann's" nation wide.
But supposedly the recipes for the two, while extremely similar, are NOT identical, with some people finding the Best Foods mayo to be more tangy.
Hence, while you're choosing which brand to use (and therefore whom to alienate regarding the name), you'll have to pick a constituency to alienate recipe- and taste-wise as well.
The back-story is that Hellman's was invented by a Mr. Hellman in a NY deli in the early 1900's. At about the same time, Best Foods mayo was introduced on the west coast. In the early 1930's, Best Foods bought out Hellman's but, by then, each brand had built a strong market share in their individual markets, so the decision was made to just leave well enough alone.
And that's worked pretty well for, what, 80 years?
I doubt they'll be changing anything any time soon.