I have never heard of "v" to be pronounced as "u". Georgian language has a peculiar feature: we say and read every letter.
That is what Georgians often say - they say ვ is always pronounced the same - as ვ. But to an English ear there are two distinct possible sounds - v and u. It varies with speaker, and with position in the word. I understand v is always acceptable, but often you hear u. Remember I am talking about v and u (w might be a better way to describe it) in English - the Georgian უ would be pronounced distinctly as a separate vowel, and is very different.
Listen carefully to Georgians saying ქვევრი. The first ვ nearly always pronounced as if there were an English u, and the second as a v. Check it on Forvo for example:
Pronunciations for ქვევრი . "Learn Georgian with Roni" on YouTube covered the point in one of his videos, but I cannot quickly find which one. I only mentioned it because the ვ in გვასალია sounded different to me in the two Forvo pronunciations I linked to. I suspect the u pronunciation is more common in normal Georgian speech, but I am not sure of that.
Incidentally, English speakers would also say t is always pronounced the same in standard British English - as a t of course. But in fact it is sometimes ტ and sometimes თ, depending on position in the word. It is the same sort of thing, but in reverse. The general point is that native speakers are not always best placed to explain (in words, as opposed to by example) to foreigners how to pronounce their own language. I am also aware that a native English speaker must be careful when explaining to a Spanish speaker!
(I agree that in the Forvo pronunciations the first syllable of the surname has the most stress, but the stress differences are not very marked, as they are in Spanish for example.)
