Name seen at 0:07 https://www.youtube.com/watch?v=-kyqE2Nq3pc
Second restaurant comes up with a google search for "全記".
Have no idea how to proceed from here.
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Although Google Translate renders the full phrase as "Full note" it renders the individual ideograms as respectively "all" and "remember".
This to me sounds very familiar to the official motto of the Province of Quebec:
"Je me souviens" - "I remember"
It may be paraphrased as conveying the meaning
We do not forget, and will never forget, our ancient lineage, traditions and memories of all the past.
In both Saigon and Hong Kong this would seem to be a reminiscence for the old colonial rule of respectively the French (or perhaps pre-1976 independence of South Vietnam) and the British.