Is a single word universally recognized?

In chapter one of my current WIP, titled QUEST, I introduce a group of antagonists bent on capturing my protagonist and taking over her business of selling alien spacecraft to world countries. I hinted to my readers that the head honcho is an alcoholic. Below, are my original sentences that I used to describe him making a rum and coke.

He poured a stiff shot of Bacardi Rum into a tall tumbler and added ice cubes and cola, watching the bubbles exploding at the rim. The knife slipped from his trembling hand as he cut a wedge of lime. Settle down, it will get better, he promised himself.

My trusted beta reader quickly pointed out that the words Bacardi Rum were redundant in that the word Bacardi was recognized universally to mean rum. After gnashing my teeth several times I decided to do some research into this enigma. I reasoned that maybe Bacardi sold other liquors under their brand name and was surprised at what my research found.

The original company dates back to the 1860's. Over the years the company purchased many different types of liquor. Bacardi has made several acquisitions to diversify away from the eponymous Bacardi rum brand. In 1992 Bacardi acquired Martini & Rossi, the famous Italian producer of Martini vermouth and sparkling wines. In 1998 the company acquired Dewar's scotch and Bombay Sapphire gin from Diageo for $2 billion. Bacardi acquired the Cazadores tequila brand in 2001 and in 2004 purchased Grey Goose, a French made vodka, from Sidney Frank for $2 billion. In 2006 Bacardi purchased New Zealand vodka brand 42 Below. Other associated brands include the US version of Havana Club, Drambuie Scotch whisky liqueur, Disaronno Amaretto, Eristoff vodka, B&B and Bénédictine liqueurs, and the Canadian alcopop Rev.

The bottom line is that Bacardi sells other liquors with their logo on the bottle and I am sure in small print a statement like Produced by the Bacardi Company. The only bottle they sell with the Bacardi label is their rum line. The two most popular rums are Bacardi Superior and Bacardi 151. With this in mind I changed the sentence to read as follows:

He poured a stiff shot of Bacardi Superior into a tall tumbler and added ice cubes and cola, watching the bubbles exploding at the rim. And if you are asking, yes, this passed by my special reader.

What two words do you have together in your manuscript that is unnecessary and how did you correct

them?