Roland's girlfriend Val is the only one of Possession's important characters who isn't given a surname. That probably has something to do with the fact that Val is such a fixture in Roland Mitchell's life—kind of like an unexemplary, familiar piece of furniture.
Val and Roland got together during their freshman year at Prince Albert College, and although Roland initially admired Val's independence and self-possession, he eventually started to feel like Val was exchanging her own identity for his:
In the early days, she had had lots of quiet opinions, he remembered, which she had offered him, shyly slyly, couched as a kind of invitation or bait. […] Later, Roland noticed, as he himself had his successes, Val said less and less, and when she argued, offered him increasingly his own ideas, sometimes the reverse side of the knitting, but essentially his. (2.8)
When Possession begins, Val and Roland's relationship is already in tatters, but Val continues to exist as a constant, dissatisfied presence in Roland's life. Because Roland is a barely employed postgraduate, Val is the main breadwinner in their dingy little home. She takes on temp jobs in the daytime and typing contracts that she completes at night, and Roland thinks of her as having split herself into two halves:
One sat silently at home in old jeans and unevenly hanging long crêpey shirts, splashed with murky black and purple flowers. This one had lustreless brown hair, very straight, hanging above a pale, underground face. Just sometimes, this one had crimson nails, left over from the other, who wore a tight black skirt and a black jacket with padded shoulders over a pink silk shirt and was carefully made up with pink and brown eyeshadow, brushed blusher along the cheekbone and plummy lips. This mournfully bright menial Val wore high heels and a black beret. (2.12)
From Roland's point of view, the spark is long gone from their relationship, but he doesn't know how to end things for good. From Val's point of view, Roland's academic ambitions and obsessions are trivial and are at least partly responsible for the fact that she has to live in a dingy apartment and work multiple jobs that she hates. Once she starts to suspect that Roland is having an affair with Maud Bailey, Val's bitterness and resentment really hit the fan.
You probably already guessed this, but Val is totally the modern-day foil of Blanche Glover, the housemate and probable lover of Christabel LaMotte. Whereas Blanche commits suicide after Christabel falls in love with Randolph Henry Ash, Val does something much healthier. Instead of pining for Roland, she gets together with the handsome young lawyer who's been crushing on her for weeks, and she gives herself a fashion makeover in true 1980s businesswoman style.
By the end of the novel, Val looks and feels amazing, which makes things a lot easier for Roland, who gets to stop feeling guilty for ruining her life.