Sileri, Siler, Seiler:
Unrelated Independent Linguistic Developments
That's a bona fide Roman family name, as in, from Rome, in Lazio Italy, with a couple hundred instances in the country.
The surname Siler in America is typically noted as a true to English phonetic rules adaptation of German Seiler (which would otherwise be pronounced as "Sailor", related in meaning but not representative enough of the cultural tie, and similar to an English family name already in existence). German Seiler meaning "one who works with rope, including a ship's sails", a family name first recorded in Basel Switzerland, from where it spread primarily with German speakers of Swiss and Schwabian descent, although this is by far not the only etymology of this name, or the word in general.
It was typical for some Italian immigrants to "Americanize" their surnames, often by adapting to a French family name or an English word with a similar meaning, and where it was possible to conform to common English phonetic rules or a meaning more familiar to other Americans by simply dropping the last vowel common to Italian family names or similar alteration, that was preferred. Steve Carell, of "The Office" fame, is an example of the latter, his family name originally from Caroselli, and now could be easily mistaken to have come from another Italian surname, Carelli. No doubt some instances of "Siler" in the United States reflect this etymology.
The German Seiler family name spread throughout Habsburg holdings by invitation/incentive to colonize regions that contained ethnic groups that held no reason for loyalty to the Habsburgs. It would be altered to various forms including the previously mentioned Siler with the Transylvania Saxons in Hermannstadt. There is a rather low incidence there today because most German speakers left the area after WWII due to anti-German sentiment.
There is also an incidence in Turkiye. Outside of the United States, the highest frequency by far is in that country. Despite the same spelling, there is no direct relation (by way of genetics, at least inside the last few thousand years) to the German incidence. That is due to an independent linguistic development, "Siler" means "eraser, cleanser" in Turkish. It is the Turkish word for the Laserwort plant, also known as Silphium, which was apparently most notable as a natural abortifacient, and was driven to extinction due to its high value.
What do all these words have in common?
They all come from Proto-Indo-European "seyl", "still, windless, quiet". Over the course of thousands and thousands of years, the meanings drifted, but all Europeans, and people in countries directly bordering Europe, and then Americans as well, have a lot more in common than a casual observer would think, and a lot more in common than most media would portray, if linguistic ties in countries as diverse as England, Turkiye, Germany, Italy and America can be traced to the same word.