The following Etymologies, unless otherwise noted, are taken from Xavier Delamarre, Dictionnare de la langue gauloise, 2nd edition, Editions Errance, 2003.
Samonios - "Month Belonging of Summer". Likely an n-stem derivative (with a suffix of appurtenance, -io-) of the Common Celtic root *samo- "summer" found in Old Irish sam, Welsh haf. Cf. Old Irish Samain "(festival of the) First of November", "All-Hallows/All-Saints day" and Mithem, Mithemain "Mid-summer, month of June", Middle Welsh Meheuin "June" (both from Common Celtic *Medi[o]-samVn [V="vowel", likely -o- or -u-]-), as well as Old Irish Cétamuin "Month of May", "First of May", "May Day" (alternate name for Beltain), Welsh Cyntefin "month of May" (both from Common Celtic *kintu-samonis "beginning of Summer"). An alternate proposal is that the root of the name is Common-Celtic *sem- "one, same, together", making it the "Month of Assembly".
Detail of Mid Samonios
Duman(n)(ios) - "Month of (religious) Fumigation"? Cf. Latin fūmus "smoke", Sanskrit dhūmah "smoke", Greek θύμος (thūmos) "soul, life, passion; anger, wrath" (also θύμιάω [thūmiaoo] "to burn, as incense", θύμα [thūma] "sacrificial offering").
Riuros - "Thick/Fat/Large month"? Possibly cognate with Old Irish remor "stout, thick, fat", Welsh rhef "thick, stout, great, large" (in which case, the original form may have been *Remros, with later shift of -e- to -i- [compare the alternation between Semi- and Simi- in Semuisonna] and lenition of internal -m-). Some scholars alternately suggest a connection with Old Irish réud, Welsh rhew "cold".
Anagantios - "Month in which One Does Not Travel", "Non-itinerant month? Composed of a Common Celtic negative prefix *an- and a an agentive noun *agant- based on the root *ag- "to go, to conduct, to lead". Cf. Old Irish ag "to go, do, conduct", Welsh agit "goes".
Ogron(n)(i)(os) - "Cold Month". An n-stem derivative of the Common Celtic root *ougros "cold". Cf. Old Irish úar, Welsh oer. The root *oug- may be compared to Armenian oyc "cold", Lithanian auksts "cold", and Latin a(u)ctumnus "autumn".
Cutios - unknown etymology. Some have compared it to the obscure Greek month name Κοούτιος (Kooutios) in the Lokrian calendar from Chaleion (which may = October-November).
Giamonios "Month belonging to Winter". An n-stem derivative (suffix of appurtenance -io-) derived from the Common Celtic root *giįamo- "winter". Cf. Welsh gaeaf, Breton goañv, Old Irish gaim "winter", Gamain "month of November" (also, a "yearling calf" [a calf that is one winter old]).
Simiuisonna (or Semiuisonna) - unknown etymology. Perhaps Common Celtic *sēmi- "half" plus *ues- "Spring(time)" or a compound containing a feminine form of the word for "sun", *sonna (see Sonnocingos below).
Equos - etymology unknown. Some scholars have connected it with the word for "horse" in Celtic languages, Common Celtic *ekWos, Old Irish ech, Welsh eb- (found only in ebol "pony", compound words such as eb-rwydd "fast/quick/ready", eb-ran "fodder", and the place name Mynydd Epynt), but there is some disagreement over this, since one would expect the form to be *Epos in a P-Celtic language such as Gaulish, in which personal, divine and place names containing the P-Celtic form *epo- are widely attested (some scholars acknowledge this point, but propose that the Calendar may contain Q-Celtic dialectal features, or archaisms dating to a time before Proto-Celtic -kw- became -p- in Gaulish; yet the Calendar does display P-Celtic words such as prinni, pog-, and peti, which argues against this).
Elembiu - "Month belonging to the Deer". From the Proto-Indo-European root *elen-bho- "deer", which gave us English lamb and the Greek έλαφος (elaphos), Έλαφιον / Έλαφιος (Elaphion / Elaphios), "Month belonging to the Deer" (called Έλαφηβολιών [Elaphebolion] "Month of the Deer-hunt" in the Attic Calendar, equivalent to March-April). An alternate form of the PIE root, *elen-, gave us Welsh elain and Old Irish elit, "doe, hind; young deer".
Aedrini(os) - Bright (or Hot) Month"; cf. Old Irish aed "fire", "heat", Greek αἰθήρ (aithēr) "bright sky, upper air, ether". Ultimately from the Proto-Indo-European root *aidh- which also gave us Latin aestas "Summer".
Cantlos - perhaps "Song month"; cf. Welsh cathl "song", Breton keñtel "lesson", Old Irish cétal.
Sonnocingos - "Sun's march"; cf. Welsh huan "sun" and Old Irish cinged "to walk, march". May not be the actual name of the intercalary month, but rather some term applied to it (Delamarre suggests perhas "sun's march = "a year").
The Gaulish calendar in historical sources
Pliny the ElderThe Natural History of Pliny the Elder states, in a discussion of Druidic gathering of mistletoe (Pliny NH 16.95):
The mistletoe, however, is but rarely found upon the robur; and when found, is gathered with rites replete with religious awe. This is done more particularly on the sixth day of the moon, the day which is the beginning of their months and years, as also of their ages, which, with them, are but thirty years. This day they select because the moon, though not yet in the middle of her course, has already considerable power and influence; and they call her by a name which signifies, in their language, the all-healing.
This comment supports the grouping of five-year Coligny calendar periods into thirty-year ages, with the loss of one intercalary month per age to more accurately align the solar and lunar cycles
Julius Caesar in The Gallic Wars states (Caesar, DBG 6.18) that days, months, and years start with a dark half followed by a light half.
All the Gauls assert that they are descended from the god Dis, and say that this tradition has been handed down by the Druids. For that reason they compute the divisions of every season, not by the number of days, but of nights; they keep birthdays and the beginnings of months and years in such an order that the day follows the night.
This is consistent with a month starting at the dark of the moon, or at the sixth day of the moon per Pliny (Natural History); it is inconsistent with a month starting at full moon.