Sini (samech-yud-nun-yud) ben Avraham.

Would this be a nickname or a real first name?>

"Sini" is a proper first name.
Sini, or Sinai, is the name of the mountain upon which
we heard the Ten Commandments- Mt. Sinai.
This was used as a first name for males in Galicia,
in particular, but probably found in other areas.

Avrohom Krauss
Telz-Stone Israel