Mostly I say "dishwasher soap" for the automatic machine - or use a brand name like Calgon or Electrosol - and say "dish liquid" for the stuff you hand-wash dishes with or use a brand and specify "Palmolive liquid."
I say "hand soap" for the bars used in the bathroom; Ivory, Pears, etc..
Washing up is what I say when I mean I am going to wash my face and hands. Confused a gentleman from Australia when I arrived for our date and asked if he "...would mind waiting a minute so I can wash up?" meaning that I wanted to use the bathroom to wash my hands and face, touch up the makeup etc, before we went out. He looked blank for a second, put it together quickly and all worked out fine.
As to Brand Names - i.e. - Xerox, Kleenex, Palmolive, Calgon, Electrosol, Ivory, Pears, Coca-Cola, Coke, Pepsi-Cola - some reporter at our paper used the word "coke" to substitute for "cold soft drink" (the meaning was clear in context) and the Editor got a letter from the Coca-Cola Company - politely but firmly worded - pointing out that Coke is a proprietary name and should not be used as a substitute for all soft (non-alcoholic) drinks! And we were just a little weekly newpaper tucked away on the New Hampshire seacoast!
The Associated Press Stylebook has tons of entries on brand names that must be capitalized ! helen of troy is 100 percent kerrekt.
In the "As" alone - to state a few - : A&P (The Great Atlantic and Pacific Tea Company,) Academy Awards, Ace (the bandages,) Actor's Equity Association; Adrenalin (trademarked name for epinephrine,)
Adventist (variant for Seventh Day Adventist,) Aer Lingus, Aeroflot, Aeromexico, Air Canada, Air Jamaica, Air France, Air India etc etc etc, AFL-CIO (American Federation of Labor and Congress of Industtrial Organizations,) A-frame, African, AIDS, Alcoa (Aluminum Comapny of America,) Alzheimer's disease, Amtrak, AMVETS, Anglican Communion, Axis (alliance of Germany, Italy, Japan in WW II.) Then, under "Awards and decorations" reporters are instructed to capitalize Bronze Star, Medal of Honor and to consult entries re Nobel Prize and Pulitzer Prize.
And I left out a lot - like holidays and agency names.
One more thing:
Pot holder - we also call "takers."
Aincha' sorry you asked?