The first thing is that "Kothri" sounds awfully similar to "http://www.uesp.net/wiki/Lore:Kothringi". Are they the same? The story places Perrif's village near a river somewhere around the Topal Bay area, so that could be in Black Marsh, where the Kothringi are supposed to be from.
Now, I suppose it's fair to assume that parents give their children names belonging to different cultures, especially cultures with a strong significance to the parents. Look at how many (predominantly Catholic) Spanish-speakers name their sons Jes?s. Another example, is that I have a sister with a French name (we're of Irish/Scottish descent), and a Portuguese best friend with an Irish name.
So, being somewhat of a human folk-hero, many parents of the various human races in Tamriel have probably named their children after Alessia. There's probably Nordic Perrifs, Breton Perrifs and who knows, there's probably some Redguard Perrifs out there.
But... in Tamriel, it seems that members of the various races tend to keep their names within their own cultural group. You don't see many Great House Dunmer with Ashlander names, and I haven't seen a Breton with a Nordic or Imperial name before. And you never see any Bosmer named "Gortwog"!
So, with that in mind, how likely is it that St. Alessia was of Kothringi descent? I haven't seen anything that outright states what race she was, just that she was born in Cyrodiil, so it seems to be assumed she was a Nord or Imperial.
I know my theory isn't exactly solid, but I figured I'd throw it out there.