According to Knopfler himself, this song is about Ray Kroc, the entrepreneur who manipulated a small California burger joint away from its two founders and into the McDonalds fast-food empire.
There's an article about it here:
In Knopfler’s portrayal, he’s a guy who sets out to “drown” his competition and does it, shaking hands and smiling all the while.
Kroc started out selling milkshake mixers to the McDonald brothers, eventually buying them out and aggressively expanding the franchise. Before composing the song, Knopfler read books about Kroc's life and business philosophy. The singer found inspiration in some quotes that were attributed to Kroc. He says, "I remember coming across a quote in a book. It was something like, 'If the opposition is going to drown, put a hose in their mouth.'"
Based on the business philosophy of Kroc, it could be a play on words, i.e., my name may be Kroc with a K, but I act like a croc spelt with a c.