There seem to be a number of examples of personal names ending in -um in the works of Plautus (apparently, they also show up in Terence1). In a discussion on Wiktionary, I found an interesting comment by the editor Smurrayinchester which makes the point that at least some of the names found in Plautus' plays "aren't Latin names any more than Nanki-Poo or Obi-Wan Kenobi are English names", and cites a text that says
there are good reasons to believe that Plautus invented many of his characters' names, especially those with humorous Greek etymologies. [...] The -ium at the end of courtesans' names is derived from an affectionate Greek diminutive; Philocomasium means "Love a Party" and Acroleutium "The Absolute End". We cannot tell how many members of Plautus' Roman audience knew enough Greek to appreciate these etymologies.
("Introduction to Miles Gloriosus", by Peter L. Smith, in Plautus: Three Comedies, (1991), p. 13)
How much evidence do we have for names ending in (i)um being used in Latin outside of fictional contexts? Naively, I would assume that if Plautus used this ending extensively in his plays, he would expect his audiences to at least be familiar with personal names ending in -(i)um, even if they didn't know enough Greek to identify all of the meaningful elements of the names.
I found a brief mention of such names in a section of "Some Roman Slave-names" by F. F. Bruce:
Greek diminutives in -ιον, mainly names of women [...] appear in Latin with the ending -ium as well [as the ending -io]. Thus Φιλημάτιον takes in Latin the forms Philematium and (as here) Philematio.
Bruce lists many inscriptional examples of names ending in -io; some examples of names written with the ending -ion; but as far as I can see no examples of inscriptions that spell a name with -ium. (There are some other sources for names ending in -io and -ion.)
- Henry John Roby, Grammar of the Latin Language from Plautus to Suetonius, Part 1, p. 106