Cahya Malfoy somewhat loathed her name. Both names. Of course, Lucius got the better name a year earlier of her, originating from Latin as, "light, brightness," and the unforgettable, "to shine," which he most certainly interpreted incorrectly to add to his obnoxiously large ego. Abraxas Malfoy, their stubbornly cold father, insisted on maintaining the theme of light, for Cahya's name, "the one who is light in the darkness," which, of course may seem a very beautiful thing, however, Lucius was already the light in the family, she was simply the one in the dark.
The Malfoy name, she considered both a blessing and a curse. Although mention of the name was enough to get them anything they wanted, the upbringing of her and her older brother was not one that she is keen to reminisce at all.
However, it would be untrue to say she despised being a Malfoy entirely. The siblings both took Abraxas' views of blood purity in opposite ways: one fully dedicating themselves to it, and one fully rejecting it. Cahya was the second. Yet, this would never be known. Openly rejecting the ideologies fed to them by Abraxas was simply not an option, there was no safe place from this, conforming was the only option. So, she did just that, she listened, kept silent and paid attention, just like Lucius.
Between '65 and 66', Lucius had left to attend Hogwarts. Leaving Cahya for a year until she could do the same. It was all a blur. Unsurprisingly, she was sorted into Slytherin when the time came, but she was careful and reserved when it came to interaction with other students, especially other houses.
In Lucius' 5th year, he became a prefect, which was not much surprise, but yet again Cahya would remain his shadow, and that was indeed solidified when she did not become a prefect in her 5th year, which certainly resulted in a strongly worded letter from her father.
Abraxas lost his job during their time at Hogwarts, the first muggle-born Minister of Magic had fallen ill due to an unknown illness which to no surprise, was seen as suspicious, and Abraxas lost his position when accused. If this didn't express the sheer dedication and extremity of the values Abraxas held, nothing else would.
She never despised Lucius, they got along very well for the most part, he was not aware of her opposing views, or that would have changed their dynamic entirely. She certainly disliked the part of him that despised people on the basis of blood status and wealth, but she couldn't hate him. She envied him, life mayhave been significantly easier if she had not developed her own morality.
Much to her dismay, this envy would follow her for the most of her life. In more ways than one.