[Oliver Pinchot]

The Russian Empire annexed Georgia in about 1801, but any Georgian
can tell you it never adopted Russian culture-- the language, religion,
cuisine etc. are all entirely different.

These daggers follow a very similar form wherever they were made. In order to establish the culture that produced them, you need to consider the decorative motifs and quality of workmanship. The hand which crafted this one was probably Chechen or Circassian. The engraved lines in the fullers are likelier to be Chechen, if they are original to it. Both Chechen and Circassian smiths worked in Tbilisi.
Tbilisi was a cosmopolitan city, and had a large, primarily Christian population of various denominations. It also had Jews and Muslims, both Sunni and Shia. Muslim smiths were likelier to sign their names in Arabic characters, while Christian smiths used Georgian or Armenian. By the 1870s, Russian was also used, due to a clientele which had shifted from local men of means to Russian military officers and gentlemen. Interestingly however, many smiths, including celebrated Georgian masters like Geurk and Osip Popov, signed variously in Georgian, Arabic, and Russian. There are examples of their work in which all three languages appear on a single piece.

Chechens, Circassians and other mountain peoples of the North Caucasus did emigrate to the Ottoman Empire, primarily after 1865. There, smiths of those ethnicities would have signed using Arabic characters.

The point is, the way a smith signed his name was first and foremost indicative of his ethnicity, not where he worked. Only with a substantial influx of foreign clients, did craftsmen in major centers begin to represent themselves as brands across cultural and thus linguistic, lines.