How do you call the emphasis of taste which you feel after swallowing food?
In Russian it's послевкусие (So to say after-taste).

Question

Answer

Aftertaste is OK, you can also say: faint taste or even flavor

Answer

Puedes llamarlo 'regusto' en español. Por ejemplo en la frase 'Esta comida deja un regusto muy dulce'.

You can call it 'regusto' in spanish. For example in the sentence 'Esta comida deja un regusto muy dulce' (something like 'this food has a very sweet aftertaste').

Answer

I say atoaji (後味:あとあじ) in Japanese.

Answer

If I understood well your question, it is about 'the persistence of taste';
am I wrong ?
(in case you are interested, in Italian it is called: 'retrogusto')