I think it's a fun name.
I will say that in the US, it was much more popular on black girls in the seventies and eighties than for anyone else. I don't believe I've ever met a white Natasha.
It's almost cliched Russian. In the 1960s, the villains on the Rocky and Bulwinkle cartoon were Boris and Natasha, names deliberately chosen because at the time Russia/USSR was considered the worst enemy the country had.
Today "natasha" is the generic term for Russian/Eastern European women who get imported into other countries to work as prostitutes, with or without their agreement.
Before you criticize a man, walk a mile in his shoes. That way, when you criticize him, you're a mile away and you have his shoes!
Steve Martin