What types of words end in "-onian"?
My understanding is that words ending in "-onian" have various sources, but it is extremely uncommon for -onian to be used as a simple derivational suffix that can be added to a name of any sort to make an adjective. Usually, a word ending in "-onian" is based on a stem that ends in "-on" (or sometimes "-o"), so the suffix can be analyzed as -ian (or perhaps in some cases -nian).
"-onian" adjectives from words or names ending in "-on" or "-one"
Many words ending in "-onian" are formed simply by the suffixation of
-ian to an English word or name ending in "-on". For example,
Oregonian, Bostonian, Newtonian, Baconian, Jacksonian are derived from Oregon, Boston, Newton, Bacon, Jackson respectively. In fact, it's probably possible to form an adjective ending in "-sonian" for any surname ending in "-son" (e.g. we also have Jeffersonian, Johnsonian, Wilsonian, Addisonian and more).
Likewise, there is Gladstonian from the name Gladstone: the "silent e" is dropped before the suffix "-ian". "Silent e" is commonly dropped before vowel-initial suffixes.
"-onian" adjectives from Latin words or names ending in "-o", "-onis"
Some other words ending in "-onian" come from Latin (or Latinized Greek) words with stems ending in "-on-". For example, Ciceronian comes from the name Cicero, which in Latin had the stem Ciceron-. This is the case for Draconian: it comes from the name Draco, a Latinized form of the Greek Δράκων "Drakōn", which had the stem
"-onian" adjectives from Latin words or names ending in "-onia"
The example "Oxonian" mentioned in the comments by GEdgar is supposed to be from a Medieval Latin form "Oxonia" based on Old English "Oxnaford", according to the American Heritage Dictionary.
"-onian" adjectives from English names ending in "-o"/the "long o" sound
Many Latin words that end in "-o" in the nominative have stems ending in "-on-". Because of this, some English words or names that end in "-o" (or just in the "long o" sound) that are not actually originally from Latin words with a stem in "-on-" have nonetheless served as the base for a derived adjective ending in "onian", such as "Buffalonian" from the city name "Buffalo", "Tobagonian" from the name of the island of Tobago, "Crusonian" from the surname "Crusoe", and (infrequently) "Roussonian" from the surname "Rousseau".
In some cases, alternative forms without the added "n" exist, like "Tobagoan" and "Crusoean". The Google Ngram Viewer indicates that "Tobagonian" is much more common than "Tobagoan", but "Roussonian" isn't even common enough to have an Ngram line, putting it below at least 4 alternative forms/spellings: "Rousseauian", "Rousseauan", "Rousseauvian" and "Rousseaunian" (in order from most to least frequent). "Crusonian" is too close in frequency to "Crusoean" (both are very infrequent) to really say which one is more common.
"Ellisonian" from "Ellis": a special, irregular example?
"Ellisonian" as an adjective related to "Ellis" is a very interesting case, and I haven't yet found any other example of an "-onian" adjective that is based on a name that doesn't end in "-on", "-one", or a "long o" sound.
I would guess that it arose due to confusion with the adjective "Ellisonian" that corresponds to the name "Ellison" (specifically used in reference to Ralph Ellison), and perhaps in part a desire to avoid the somewhat awkward sound of "Ellisian".
Personally, I would prefer to use "Ellisian", which does in fact exist, as the adjective corresponding to "Ellis" in all contexts.
An example of "Ellisian":
In spite of the fact that he sprinkles his Rogerianism with an occasional Ellisian* onslaught (strange juxtaposition but apparently successful with me), this man is a concrete representation of every concept you deem necessary for a successful therapeutic relationship.
[...] *Reference is to Albert Ellis, the originator of rational-emotive therapy.
(p. 216, A Way of Being, by Carl Rogers)
In general, "Marxonian" would only be expected if the base name were something like "Marxon", "Marxo" or "Marxonia". Real-life examples of "Marxonian" appear to be extremely uncommon and the examples I found on Google search seem to be used in a variety of ways:
as a term used to refer to fans of the Marx Brothers comedians in a number of posts on Mikael Uhlin's Marxology @ marx-brothers.org:
In one case, as a portmanteau of "Marx" and "Oxonian":
...a terminological inertia that harks back to his Marxonian (from Marx and Oxford) period
("On 'September 1, 1939" by W. H. Auden", by Joseph Brodsky, in Less Than One: Selected Essays by Joseph Brodsky, p. 338)
In contrast, the form "Marxian" not only exists, but is common enough to be listed in a number of dictionaries. Merriam-Webster defines it as "of, developed by, or influenced by the doctrines of Marx · Marxian socialism".
The phenomenon of "libfixes"
New suffixes do sometimes arise from reanalysis of the formation of older words, particularly in playful contexts where people are just trying to create words that sound right rather than words that other people will necessarily find "correct". Arnold Zwicky's blog post "Libfixes" proposes this name for the phenomenon and gives some examples (such as -licious and –tacular).
Some "libfixes" have become very well known, such as -holic. However, "-onian" doesn't seem to have attained much popularity yet as a libfix. The only possible examples I've been able to find aside from the ones discussed above are obscure and seem to occur mainly in the context of self-aware wordplay:
"Rockonian" as a playful adjective referring to Joseph Rock:
Rock clearly understood the Asian concept of "face" and in true Rockonian style, he once said, "You've got to make people believe you're someone of importance if you want to live in these wilds" (Sutton 1974, 15).
("Filming Rock", by Paul Harris, in "Classifying Joseph Rock: Metamorphic, Conglomerate, and Sedimentary" by Alvin Yoshinaga, He Jiangyu, Paul Weissich, Paul Harris and Margaret B. Swain, in Explorers and Scientists in China's Borderlands, 1880-1950, edited by Denise M. Glover, Stevan Harrell, Charles F. McKhann, Margaret Byrne Swain, p. 137)
"Wickonian" (Urban Dictionary entry)
- Pertaining to that which is wickid(slang)
[...] by fantasticmrK March 26, 2009
It only received 5 upvotes and 1 downvote as of February 15, 2018 (I accidentally voted on it today when I visited the page).
a few examples of "jerkonian", apparently used as a synonym for "jerk" or "jerkish".
BTW, CMP, why is there no “Credo House Forum” so that we may discuss these things more deeply. I think you guys have done a wonderful job at setting an example and tone that may facilitate more “non-jerkonian” discussion.
(comment made by Chris Echols, 2011-11-05 at 6:39 am in response to the blog post “Do Roger Olson and I Worship the Same God?”)
By no means was I rude to the girl but this is a jerkonian policy at SFNE. Nevertheless, this is an amazing ride!
(from "Six Flags New England: Visit #1: Date: 6/13/15" by Kevin Michaels, on themeparkmaniacs.com. In this case, "jerkonian" might be a portmanteau of "jerk(ish)" and "draconian".)
"Floodonian" as a supposed adjective corresponding to "Flood" in a post made on the halo.bungie.net forums: Subject: When did "Floodonian" become "Floodian"? The original post was made 02.02.2012 5:16 PM PST. The subsequent posters disagree that "Floodonian" was ever in common use.
Differences between words ending in "-ist" and "-(i)an"
Figuring out when to use "Marxist" vs. "Marxian" should be covered to some extent by the answers to the related question identifed by Edwin Ashworth: Usage of -ist and -ian, when to use which?