[Mrs. Glover's] strapping son was a straightforward George. "Tiller of the soil, from the Greek," […] and George was indeed a plowman on the nearby Ettringham Hall estate farm, as if they very naming of him had formed his destiny. Not that Mrs. Glover was much given to thinking about destiny. Or Greeks, for that matter. (4.51)
If a person's name defines them, we worry about celebrity children like Pilot Inspektor and Moxie Crimefighter. Actually, on second thought, those kids sound kind of awesome.
Motherhood was [Sylvie's] responsibility, her destiny. It was, lacking anything else (and what else could there be?), her life. (6.47)
If Sylvie sees herself as a mother by fate, why isn't she a better one? She lets Maurice run wild, for instance, and she disparages Ursula's lack of morals (in her opinion) in the timeline where Ursula gets raped. For someone who defines herself as a mother, Sylvie isn't very nurturing.
How on earth had [the parcel] got here? There were no trains running and Pamela was almost certainly snowed in. Even more puzzling was how her sister had managed to dig up this wintry harvest when Earth stood hard as iron. (18.8)
This is a good question: How does Pammy's parcel get all the way from Fox Corner to Kensington? Could it have been delivered by the hand of fate?
"Fate isn't in your hands. That would be a very heavy burden for a little girl." (20.91)
Tell that to Buffy, Dr. Kellet. In one of Ursula's later lives, she does take the burden of fate on, and practically crumbles under its weight. Feeling responsible for the future of the world is impossible for anyone to bear, at any age.
"Amor fati. […] A simple acceptance of what comes to us, regarding it as neither bad nor good." (20.107)
This might just be the main point of the novel. Ursula isn't happy until she accepts this theory: that what happens, happens. Or, in reality TV show lingo: It is what it is.
"[Harold] had a scrap with […] Edwina about predestination."
"She believes in that? I thought she was Anglican."
"I know. She has no sense of logic though." (21.11-13)
Fate doesn't follow any sense of logic. It's not logical that Ursula is born and reborn, and can only vaguely remember echoes of certain events—but it's true.
Was this her fate too, [Ursula] thought, contemplating her bespectacled reflection in the mirror above the fireplace? Would she, too, end up as an old maid? (21.171)
This is less fate than fear of being single, although perhaps it is her fate to be an old maid. It seems that the only lives she's happy in are the ones in which she remains single.
A Todd and a Fuchs—a pair of foxes. Had fate intervened in her life? Dr. Kellet might have appreciated the coincidence. (24.79)
One of Ursula's better relationships happens with a man who has basically the same last name as she does, but it's still not perfect.
"He's always been a politician. He was born a politician." No, Ursula thought, he was born a baby, like everyone else. And this is what he has chosen to become. (24.158)
As someone who feels she has control over her own life (lives), Ursula believes in free will, of course. She doesn't think Hitler was born to be evil; she thinks he chose that path.
"Roland," Sylvie said. "I've always rather liked that name. The Song of Roland—he was a French knight."
"Died in battle, I expect?" Hugh said.
"Most knights do, don't they?" (26.26-26.28)
Could they be dooming the baby to death by naming him after the character in The Song of Rolandwho blows a trumpet so hard that he dies? Izzie's son doesn't live past the age of five.