Following @Randal'Thor's suggestion, I am posting a partial solution to my question (the meaning of the "V"), together with some speculative answers to the remaining part (the meaning of the "R"). If anybody finds a more authoritative answer for the "R" I would be happy to accept their answer though.
Rereading the text in detail when Marsch first meets the Annese beggar "R.T." we find the following dialogue:
[the father] exclaimed, “Ah, you are a doctor! Look, Victor, our
visitor is a doctor of philosophy!” and held the card for an instant
in front of the boy's eyes
So his son is called Victor, and thus the meaning of the "V" initial is indeed revealed, although in a very subtle way.
This just leaves the "R". Ultan's library (a web resource for the study of Gene Wolfe) makes the comment:
V.R.T. is Victor R. Trenchard. If the ‘R’ of his middle name is
Rodman, as some people have suggested, this is an additional
correspondence, being author Gene Wolfe’s middle name
I do not know who the "some people" are making this suggestion, but it is interesting to note that the fan-base do not have a commonly-accepted answer. So unlike the "V" which came down to noting a particular sentence fragment, it is probably the case that the "R" is unspecified in the book. In that case "Rodman" seems as good a guess as any.
Some go further though. Robert Borski's Cave Canem website is now hosted at the wolfewiki and contains an entertaining (though highly questionable!) account of how he deduced that the "R" stands for "Roy". The V.R.T. exercise book contains the text "Rm E2S14 Seat 18." Treating the numbers as a cipher yields R E 2 S N R, which (he asserts) can be interpreted as "2 Roy Emersons, son/senior", since Roy Emerson is the name both of Gene Wolfe's father and first son. Based on this he claims that:
Can there now be any doubt that VRT is named after both Gene Wolfe's
father and son and stands for Victor Roy Trenchard?