The names you are asking about are not necessarily nicknames, although they could be. They look like female names, coming from the word "Serene". They may also come from words in other languages, or just be made-up spellings. (Serena Williams is a famous tennis player.)
My grandmother was born in Hungary--her name in Hungarian was Szeren (pronounced Se-rain). This was a popular name in Hungary in the 19th century,although I understand it is rare today. When she came to America, Grandma changed her name to Sarah, because it was easier for Americans to pronounce. By the way, I never heard that Patsy was a nickname for Martha--it doesn't seem to be related. (My legal name is Patricia, but as a child I was called Patsy--I no longer use that nickname, prefering Pat instead.