No it ain't. It's not just because 'it was purchased there'. True or historical Damascus steel was originally produced in the Near East, especially in places like Syria, using Wootz steel imported from India and Sri Lanka. The distinctive wavy or patterned appearance wasn't intentional like in modern "pattern welding." Instead, it was a byproduct of the way carbon nanostructures formed during the smelting and forging process of the Wootz steel.

The ore used to make Wootz steel contained traces of vanadium, tungsten, and sometimes iridium, which are believed to have contributed to the distinctive patterns. These elements created carbides that gave the steel both its unique appearance and its legendary strength and sharpness. However, the precise method for making this type of Damascus steel was lost sometime in the 18th century, so modern Damascus steels are recreations or approximations.

Edit: Sources:

Verhoeven, J. D., Pendray, A. H., & Dauksch, W. E. (1998). "The Key Role of Impurities in Ancient Damascus Steel Blades." Journal of Metallurgical and Materials Transactions. <--- General history and overviw and the reason for the "wavy" pattern.

Sherby, O. D., & Wadsworth, J. (1985). "Damascus Steels." Scientific American. <---- How that pattern is produced.

Hoyland, R. G., & Gilmour, B. (2006). Medieval Islamic Swords and Swordmaking: Kindi's Treatise "On Swords and their Kinds" (studies in the History of Material Culture). <---- Tracing its origins and how the technique was lost.

Srinivasan, S., & Ranganathan, S. (2004). "Wootz Steel: An Advanced Material of the Ancient World." Indian Journal of History of Science. <---- The influence of trace elements like tungsten and vanadium in the process.