Neo-Valarin prefixes and suffixes, with others

(long vowel) -z - nominative e.g. A3ûlêz "crafter", *A3ûlân "to craft"
-unum-(suffix) - plural e.g. Ayanûz "Ainu", Ayan-um-ûz "Ainur"; Mâxanâz "Authority", Mâxan-um-âz "Authorities"

*-ân - present tense e.g. Akaš-ân "He [Eru Ilúvatar] says"
*-ûðân - past perfect tense ("has/had been X-ed") e.g. Dušaman-ûðân "marred, has been marred"
*-ai - present continuous tense ("-ing") e.g. Ošoš-ai "spuming, foaming"
*-aiš - simple past tense ("X was/used to be Y") e.g. Aman-aiš-al "unmarred, [that] used to be unmarred"

*-al - adjective e.g. Amanaiš-al "[it was] unmarred" *Aman-ân-al "[is] unmarred"

Assuming that Black Speech is actually a corrupted form of Valarin ("nazg/ring from anaškad, ghâsh/fire from igas/heat") with some other words thrown in, here are some words that are being reconstructed on that basis:

-ishi (in) - *-ši (in, into) | burzum-ishi (in the darkness) - *pûruz-umâz-ši (into the dark-ness)
-at- (to, for) - *-at- (to, for (this)) | krimp-at-ul (to bind them) - *girimaphân-at-ulûz (to bind them)

-ul (them) - *-ulûz (them, they) | gimb-at-ul (to find them) - *gimabân-at-ulûz (to find them)
-ûk (all) - *-ûkûz (all) | thrak-at-ul-ûk (to bring them all) - *aþarâkân-at-ul-ûkûz (to bring them all)
-ulûk (them all) - *ul-ûkûz (them all, all of them)

-um (ness) - *-umâz (-ness/-hood)
agh (and) - *a3a (and) | agh burz-um-ishi (and in the dark-ness) - *a3a pûruz-umâz-ši (and into the dark-ness)

Assuming that this Orcish variant of Black Speech is still Black Speech, we could attempt to reconstruct some more words for Valarin:

"Uglúk u bagronk sha pushdug Saruman-glob. Búb-hosh. skai!" (translation used from this section)

u (to) - *ut (to) | Uglúk u bagronk (Uglúk to the torture-chamber) - *Ugulûkûz ut baga-ronokôz (Uglúk [shall be sent] to the torture-room)
sha (with) - *šâ (with) | sha pushdug Saruman-glob (with stinking Saruman-fool) - *šâ gilobôz bušudugal Sarumanâz (with [the] stinking fool [of] Saruman/Curunir)

More Valarin reconstructed names

As for the Maiar, only Ošošai's (Ossë) Valarin name is known. Here are some Valarin names reconstructed for many of other known Maiar, helpers and servants of the Valar:

Noldorin Quenya - Neo-Valarin - Primitive Quenya/Valarin/other sources

Five Istari:

Olórin (Gandalf) - Ibrîgûlôz (silver servant) - Ibrî ("silver", from Ibrî-niðil-pathân-ezêl "*Silver-flower-leaf-green", Valarin); Gûl ("servant, wraith", from Nazgûl "Ring-wraith", Black Speech)
Curumo (Saruman) - Igwiša3ûlêz (white crafter) - Igwiš ("white"); A3ûlêz ("crafter", as Saruman was more into machines, being a Maia of Aulë, both Valarin)
Aiwendil (Radagast) - Âyawin-gimabâz (bird-finder) - Aiwē-n(d)il ("small bird-lover", Primitive Quenya); gimba- ("find", Black Speech, almost corresponding in function to "-ndil", in that Radagast seeks to see and be with the birds and wildlife of Aþâraphelûn)
Alatar or Morinehtar - Pûruzu-bagêz (darkness-destroyer) - Búrz ("darkness", Black Speech); bag ("torture", Lower Black Speech, third translation)
Pallando or Rómen(s)táro - Barâdâz-âyanâz (east/raised-helper) - Barâdâz ("raised", used for "east", as this is from where the Sun has been "raised" into the sky, Neo-Valarin from Primitive Quendi Baradá "lofty, sublime"); ayanûz ("Ainu", used for "worker", as the Ainur worked to create and sustain the universe, Eä, Valarin)

Evil Úmaiar:

Sauron - Aþa3uzônôz (the cruel) - Saura ("cruel", Primitive Quendi) and Þauza ("foul", possibly Vanyarin Quenya)
Mairon (Sauron) - Mayazônôz (the admirable) - Mairon ("admirable", Quenya)

Other Servants of the Good Valar:

Eönwë - I3ônowêz (herald) - (no known etymology)
Ilmarë - Gili-mâz (star-light) - *Gil(ma) ("starlight", GIL is related to the root for Ilmen, "Space (for stars)", Primitive Quendi and Quenya); -rë (feminine suffix)
Arien - Tulukh-igas (yellow-heat) - Tulukh ("yellow, gold"); Igas ("heat", both Valarin)
Tilion - Ibrî-3arôz (silver-horned) - Ibri ("silver"); Arôz ("horn", based on Arômêz, "horn-blower", both Valarin)
Uinen - Uyu-ninêz (seaweed-maiden) - *Uy ("seaweed", unknown non-Elvish language, possibly Valarin); *Nen ("water", Quenya)
Salmar - Salimâz (harp-man) - *Salma ("lyre, small harp", Quenya)

Reconstructed Valarin Names

We already have the original Valarin names for only four of the Valar: A3ûlêz, Arômêz, Mânawenûz, Tulukha(š)tâz, and Ul(l)ubôz. With some aspects of Tolkien's other languages, such as Khuzdul and Black Speech (itself partly based on corrupted Valarin), being reconstructed by people like David Salo, why not attampt to reconstruct the Valarin names of the other Valar as well?

Noldorin Quenya - Neo-Valarin (and meaning) - sources in Primitive Quendi

Varda - Barâdâz (raised, she-who-raises) - Barád/Baraþ (sublime, lofty)
Yavanna - Aya-banâz (fruit-giver) - Yab-an(t)a (fruit-giver)
Mandos - Mâna-dostôz (blessed keeper) - Man-dostŏ (custody-castle)
Námo - Nâmâz (judge) - Nam (judge, ordainer)
Nienna - Niyennâz (mourner) - Nei (tear)
Lórien - Lôriyenêz (dream-lander) - Lor (slumber, dream)
Irmo - Irimôz (desirer) - Írë-mo (desirer)  -  (the Primitive Quendi terms for this are lost, so Quenya terms from http://www.realelvish.net/book_names.php are used instead)
Estë - Ezedêz (rester) - Ezde (rest)
Vairë - Wiyarêz (weaver) - Wir/Wey, Weiré (Weaver, Weave)Vána - Wânâz (beautiful) - Wána (beauty) - (no Primitive Quendi term available)
Nessa - Neššai (vigourous) - Nessa (young) - (no Primitive Quendi term available)

Melkor - Belekôrôz (mighty-rising) - (M)Bel(ec) + órë (large, mighty + rising)