Okay, so in doing some digging I found a few things.
First, Caffeina is most definitely not an ancient Roman Goddess. Coffee itself wasn’t a thing in Rome or even ancient Greece. Wikipedia tells us that “The history of coffee dates back to centuries old Oral tradition in modern day Ethiopia…” but evidence of its consumption has not been found prior to the 15th century. It wasn’t until after the 16th century that coffee was traded from Ethiopia to the Middle East, followed by the rest of Asia and then Europe. This makes it highly unlikely that a goddess inspired by coffee is ancient. Wikipedia
One of the earliest pieces of writing on Caffeina seems to come from between 2006 and 2007. It appears to be a sort of tongue-in-cheek piece of prose about the modern-day reliance on caffeine and coffee. Here’s a quick excerpt of the writing written by Terrence P. Ward.
It is by Caffeina alone
that I set my mind in motion.
By the Beans of Java,
my thoughts acquire speed.
The hands acquire the shakes,
the shakes become a warning.
It is by Caffeina alone
that I set my mind in motion…
– Attributed to Isaac BonewitsCaffeina, Goddess of Untamed Energy, comes to many of us through her sacred plant, coffee. This Dark Mother is bountiful, but must be honored regularly lest our faith waver. She springs forth, daughter of Earth and Sun, ready to deliver her father’s touch to any who are willing to accept it…
The worship of Caffeina in Her cup spread more quickly into Europe and the Americas. Coffee was cultivated in more and more areas, and both its praise and condemnation managed to make the Goddess of Untamed Energy a more widely-honored divinity. In the 1990s her hold over the secular world was secured by a marketing program rolled out by Starbucks Coffee Company: stores would be decorated in colors that denote one of the four essentials to good coffee, Grow (earth), Roast (fire), Brew (water), or Aroma (air). Quietly Caffeina, in Her guise as the Starbucks Siren, had lifted Her worship to new levels in the United States and worldwide…
Like any Goddess or natural force, Caffeina must be treated with respect due Her station. One does not flippantly disregard Her power for long before one has a series of sleepless nights during which contemplation of such disrespect is likely. Sufferers of narcolepsy, clouded thoughts, and lethargy would do well to give Caffeina her due. Likewise, insomniacs, jittery people, and those who speak too quickly should not be so quick to condemn this Goddess, when understanding Her would more likely help them find the answers they seek. Witchvox via The Wayback Machine
Now, just because Caffeina seems to be what’s called a “Found Goddess” (as @Amethyst said) doesn’t make her any less worth honoring if that’s what you want to do. I would just heavily, heavily caution against saying she’s a Roman Goddess because that’s 100% historically inaccurate.
I would say Caffeina would be an egregore-turned-deity for some people. Here’s some info on egregores.
Egregore (also spelled egregor; from French égrégore, from Ancient Greek ἐγρήγορος, egrēgoros ‘wakeful’) is an occult concept representing a certain non-physical entity that arises from the collective thoughts of a distinct group of people. Wikipedia
What this basically means is that if enough people believe in something and put enough energy behind it, that energy becomes the thoughtform representative of the thing believed in. In this case, if enough people believe Caffeina to be a deity of energy, stamina, and focus, all relating back to coffee and caffeine, then she exists and has been created as a thoughtform.