Branding is everything. Everybody recognises the Nike swoosh, the Apple logo, or the McDonalds arches, because they’re everywhere. In England during the time of the Mary Rose, the most prominent image was the Tudor rose, symbol of the Royal Family, and of the king, Henry VIII.
While the Tudor rose appears to have been absent on the ship’s structure (give or take the emblem), it does appear on quite a few of the items found on board the Mary Rose, and even then on a few personal items!
It seems odd that the symbol of the Royal Family would appear on normal people’s belongings, but is it any stranger than the flag of St George or the Royal Arms of England appearing on everything from cufflinks to underpants? A bit of national pride can go a long way, and to them, the Royal Family, and the Tudor rose itself, represented England herself (and a look at the ‘Visit England’ website would suggest that it still does!).