By giving some characters real names and others silly ones or mere numbers, Poe is allowing his narrator, the highly ridiculous Thomas Smith, to illustrate his lofty, supercilious habit of classifying things and people in a false show of mastery and authority. In other words, the names parody the silliness of distinctions made in both high society and academic scholarship. Keep in mind that "Lionizing" is a comedic story; it's supposed to be ridiculous and funny.
You might actually classify the characters in this story into three groups:
1. Those with real names or titles, such as Blackwood, Mrs. Bas-Bleu, and Signor Tintontintino. The narrator deems these people important and intelligent and allows them to go by their actual names.
2. Those with "blank" names, like the Marchioness of So-and-so and the Earl of This-and-that. The narrator glosses over these people as if they have only a marginal importance.
3. Those with numbers for names, which occurs only in this single conversation toward the end of the story:
"‘Bête!’ — said the first.
‘Fool!’ — said the second.
‘Ninny!’ — said the third.
‘Dolt!’ — said the fourth.
‘Noodle!’ — said the fifth.
‘Ass!’ — said the sixth.
‘Be off!’ — said the seventh."
Note that it's the narrator's supposed friends who get labeled with numbers--they matter very little to him, ironically, while the perfect strangers in high society matter enough to merit their own names. Regarding his friends, all that matters to the narrator is that they called him a beast, a fool, and so on when they found out that he'd shot the nose off the Baron.