Intentions behind Spector's actions in the finale of season three?

It's a way to keep in control of his own life, to have the last word. He was caught, his identity revealed, his fate was decided by Gibson / the doctor.

In an interview the series creator said

I’m aware of the fact that, again in reality, quite a few of these individuals do, at that point in time, take the opportunity to take their own life because they want to maintain some kind of control, even if it’s the ultimate self-destructive control.

The desire to control the situation, the desire to undermine any sense of Gibson getting satisfaction.

^{S3 E3} Evidence from the lock-up shows the murder of a young brunette woman in London, a decade ago, for which David Alvarez (Martin McCann), a friend of Spector's, is serving a sentence.

^{S3 E5} Anderson and Ferrington go to London to speak to Alvarez about the murder of the brunette woman in 2002. Alvarez recounts the horrific sexual abuse the boys experienced by the staff members at a boys' home where they both resided. He notes that Spector spared him from the worst of the abuse.

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^{S3 E6} hanging himself on the back of the bathroom door with a plastic bag over his head and the belt. His mother committed suicide in a similar manner on her bedroom door when Spector was eight.

_{— Wikipedia, List of The Fall episodes: Series 3 (2016).}

Recall that, when interrogated by the police, he firmly denies any abuse (and thus any trauma, physical or psychological), alleging that a self-imposed lack of personal hygiene kept him safely at bay from ever becoming the target of any such perversions and twisted desires; needless to say, the interview with one of his former friends revealed a picture diametrically opposed to that painted by him.

Since he would eventually come to embody his abuser(s),¹ the intense rage projected at them was thereby ultimately turned inwards, against oneself, inevitably ending in suicide; previously, it was detoured or derailed against the women he tortured and killed, but, with any such possible outlets for his savage and uncontainable fury having been taken away by his incarceration,² the plot heads steadfastly towards the only logical conclusion: its (main) character's tragic outcome.

¹_{Unlike Stella Gibson's colleague and former lover, interpreted by John Lynch, who seems to have spent his entire professional life putting men like them away behind bars.}

²_{Among the last explosive expressions of this incontrollable anger (re)directed at women is Stella Gibson's brutal physical assault.}