The Sanskrit (and Hindi) sound is actually a labiodental unaspirated consonant, and most people write it as a v, which in English has slightly more aspiration: the w is probably to avoid that. In any case, in Bengali, it is actually pronounced b, so all that is rather academic. The ri is actually the vowel R (as in grrrr, only shortened to a short vowel length), it is ri in most parts of north India, but ru as you come slightly south of that. The d and dh are dental, unaspirated and aspirated, the i is short, and the a is long open (as in English car).
vR is actually quite common in Sanskrit, but the reflex of the sonorant R is often a consonantal r in other Indoeuropean languages, and the conjunct (or sonorant) sometimes appears as a zero-grade ablaut. The Sanskrit v is often cognate with Germanic w. As far as I know that wren is of unknown etymology beyond Germanic (and it used to be werna, the current form is a metathesis), and writing is a new concept, for which I don't know where the w- comes from (the closes Sanskrit is rikh, to scratch), but wrath does go back to ProtoIndoEuropean wer-/wert- to turn, which is also reflected in Sanskrit vRt/vart to turn/revolve/roll.
In any case, the root is vRdh, to increase (grow, be abundant, grow old) appears already in the Vedic period, of unclear origin, but sometimes connected with the Indo-european base wrad- apparent in English root (plant part), radix, and radish. It with the noun-forming suffix -ti (vRddhi = growth, often figuratively, and also in many technical terms), followed by the possesive (or `has' or `causes') suffix -mat: vRddhimat (apart from a technical term in grammar) means somebody who possesses growth, or becomes powerful. The masculine nominative singular is vRddhimAn.