If you think this is weird, then you should study the Roman republic. A huge portion of male aristocrats would have the same name as their father and there were maybe a dozen first names that you find on all important people put together. Old Constantinus here is actually being quite imaginative, in part thanks to living several hundred years since that time. I can't say for sure that there isn't any significance to the names, but these things certainly weren't uncommon.

I do have a related follow-up question though. The man himself was called:

Flavius Valerius Aurelius Constantinus Augustus

and his sons:

Flavius Claudius Constantinus Augustus

Flavius Julius Constantius Augustus

Flavius Julius Constans Augustus

Could someone smarter than me explain how the first son has Claudius in his name, and the other two have Julius, when their father had neither? Something to do with the name of the Julio-Claudian dynasty becoming titles like Caesar and Augustus did? I got the names from Wikipedia, so are they just making a mistake?

We had an interesting discussing a few weeks ago on honorary naming in the Late Roman Empire (which actually tied in with Constantine). As for your question, I am not sure there is more to it than a very decided dynastic project, but I would be interested to see a more daring take on the question.

You didn't mention Constantine's first born son, Crispus. He was groomed and was fully able to be Constantine's successor before he ordered Crispus, then his own wife Fausta, to be executed. No one knows why Constantine ordered the executions, though the most widely believed story is that Fausta tried to seduce Crispus and, upon being rejected, told Constantine that Crispus tried to rape her.