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Surname based on the male forename Karim, or possibly Abd-al-Karim. Karim is Arabic and means "generous", Abd-al-Karim means "slave of the generous one", another way of saying worshipper of God. The -ov endig is, of course, the Russian surname ending, adopted throughout the old Russian empire, later USSR.
The peoples of the Central Asian republics are mainly Muslims or descendants of Muslims. Arabic and Persian names are common, e.g., Aliyev (Ali), Akhmatov (Ahmad). The names are often mangled until almost unrecognisable because of the Cyrillic (Russian) alphabet in which they are written.