St. George:
The photo in your link shows three, possibly four, yards on each mast - kind of hard to tell when the point of view is close to directly abeam. The Wikipedia article for RMS Rhone has an image as I described above that appears to be authentic since the company and ship's names, ship dimensions and capacities are a part of the image. If I was building a model of RMS Rhone I would have to choose the Wiki image over the one in the St. Thomas Historical Society web article. I've seen plenty of photos on similar websites that (just as an example) identified an image of a three masted ship as being of a specific four masted barque.
The image that I posted - and you are attempting to identify - is of similar provenance. It's from a contemporary lithograph by a well known lithographer in the collection of a prestigious museum with the company name, ship name, captain's name, and cargo and passenger capacities as a part of the lithograph. Of course I cropped that info when I cropped the registry flag.
I'll re-cap the hints I've given: It's S.S. [something], it's not named after a person and it's not of US registry, plus those I gave above.
I hope you're all having "fun" with this one.