What is the name of first Arabic alphabet?

There isn't a single "first" Arabic alphabet in the sense of a specific name. The Arabic alphabet has evolved over time, and there's no definitive starting point.

However, we can trace its origins back to the Nabataean script, which was used by the Nabataeans in the 1st century AD. This script is considered a direct ancestor of the Arabic alphabet, and its letters formed the basis for the later development of the script.

So, while there's no specific "first" Arabic alphabet name, Nabataean script is recognized as the crucial predecessor.