Depends what you mean by "myspace in the name"
If the site is helping to promote the MySpace network - codes or something - then you might be OK. If the site is a typo, parked or "myspace sucks" then I'd expect News Corp to actively pursue it.
Ideally, if you're promoting their network, you'd think it'd be OK but maybe not. It is still a trademark and it all depends on what sort of company you're dealing with. In this case, News Corp, I'd expect them to take action more often than not and especially more often than the previous owner.
Just bear in mind it is their trademark and they can pursue it anytime they like. There's nothing to stop them closing you down and taking your domain even if you are promoting their site.