Suki is a humble term, a term of endearment and a sentiment (but not necessarily that specific word) found in many Asian cultures including Vietnamese, also politeness. It truly means "I beg your pardon, but we are not quite as good as you but we try our best". I don't know the pure Vietnamese term for it (whatever Vietnamese I learned was fully tempered with a Chinese dialect, as my friends were in a mixed culture family and had sort of their own language, a mixture of the two).
Do you have a citation or reference for this?
And do you think that's what "We Suki Suki" is really intending to mean in the store name?
Urban Dictionary says -
In Japanese, "suki" can mean several things, but it is most commonly used as the word "like."
Sometimes it can be used as slang for the word "love" as well, since in Japanese, "daisuki" means "to like a lot."
So, If you "daisuki" something that means you like it a lot.
Japan has a lot of slang for their phrases (as do most languages), so people who slang their words, or who don't like long sentences/words don't bother to say "daisuki" would just say "suki."
Also, "suki suki" almost seems like the "cute way" to say you like something!
AND, it is NOT a blowjob; spell it RIGHT - it's SUCKY SUCKY, not SUKI SUKI. Please see Sucky! Sucky! Five Dolla! for the right reference!!!