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I haven't read Blood and Gold and don't really care to, honestly! I know that Marius' official canon backstory is that he is the illegitimate son of a Roman citizen and a Gaulish woman, but I've heard conflicting information on if she was free or a slave and if so a concubine of his father's, but the name Marius would seem to imply to me he was either takng a name he had no legal right to, wholly legitimate, or a houseborn slave: slave children of the master could be freed and afforded citizenship and inheritance immediately (vs a slave who was not your own child or brother had to be 30 years old in order to be freed), where an illegitimate birth to a free Gaulish woman would not afford Marius Roman citizenship during his human lifespan, nor legitimate access to the name of gens Maria, unless he was adopted later in life!
Marius is a "last name" or family name, and Armand's use of it in the Theatre des Vampires posters is entirely correct! Freed slaves (who by law have no family) became a legal member of their manumitter's gens and took their name in totality, using their personal name as a cognomen. Using Amadeo as an example, had he been purchased back in Marius' mortal life (let's assign Marius the personal name Gaius, abbreviated C., for the purposes of this), then Amadeo in slavery would be legally called Amadeo Gaii servus or Amadeo C. s., but had he been legally manumitted, his name would become C. Marius Amadeo C. l., Gaius Marius Amadeo Gaii libertus, and known likely as Marius Amadeo. This is the same format we would expect Marius' own name to take (for a freeborn citizen, we see instead of "Manumitter libertus", "Father filius"), but of course we don't know his father or potential manumitter's name.
I chose to refer to Marius as being of Spanish extraction not to overtly go against Anne's vision (we must remember Rome encompassed a huge swath of territory including parts of North Africa, and all of those very ethnically diverse people are in fact Romans - Marius' father could be from most anywhere and look like most anything) but because there are some very entertaining Spanish Marii in the general span of Marius' lifetime, and it pleases me to imagine a connection. First there is a man called "Pseudo-Marius" despite the fact he probably was a member of gens Maria (if perhaps not the legitimate grandson of the man he claimed), who was a wealthy man with ties to Julius Caesar and who was murdered on the orders of Marc Antony. Second is a Sextus Marius, in the early 30s CE one of the wealthiest Romans in Hispania, who according to Tacitus was accused of incest with his daughter and executed by being thrown off the Tarpeian Rock. There's no reason to specifically claim the IWTV adaptation's Marius is this particular Sextus Marius of antiquity, but there's also no reason not to. I think his continued difficulty in trying to marry Pandora could be very easily tied to incest, and then he'd have that in common with Lestat! :)