It would cost nothing?
Are you aware of how much a rebrand costs?
We're talking billions.
The earliest archaelogical (material) evidence for the Magen David (Shield of David)
in Judaism comes from Sidon in 7th CE, but afaik didn't gain popularity in diaspora communities until around 12th CE. Prior to that, earliest evidence for use of that symbol in that region dates to 7th BCE and there is no proven connection to the real David, just myths and legends (but every culture has these myths and legends as part of their tradition). By early 20th Century, the Magen David is used by all and sundry diaspora Jewish communities to denote their idenity as Jews as they participate in social events, especially sports.
However, and this is a very big however, this symbol is NOT exclusively Jewish. It's use is found throughout many, many cultures with each culture assigning it's own significance to the six-pointed star as a sign. I'm told it does have significance to all Abrahamic religions - Judaism, Christianity and Islam (great lovers of geometric shapes!). If you look hard enough, you'll find it's use throughout the middle and far east, beyond Judaism - to what's considered to be the first monotheistic religion: Zorastrianism (who were afaik, the originators of the middle-eastern flood-myths).
It was used throughout Persia - and recorded as being used during the time of Alexander the Great, especially in relation to metalurgical methods, but not exclusively, being a symbol widely used throughout the middle east region. It's used in Buddhist temples. It's used in Tantic yantras. It's used throughout India and Tibet.
This symbol is NOT exclusively Jewish, whatever you might think, although when Jews talk of it, they call it 'Shield/Star of David'.