As long as that very description is spelled out clearly near the top of the job ad, it doesn't matter terribly much (within reason) what you call it - job searchers will try various different strings to find it. Personally, I'd call it an ops role, however.
In general, most of the issues I've seen with these sorts of roles aren't the naming of them but rather the third bullet in your list. Having an ops role that's responsible for all the problems with software they didn't build and weren't allowed to have meaningful input to the design/implementation of isn't healthy. It sucks up their time and energy fighting fires they didn't create and likely aren't really empowered to fix. This is the problem with this role (as often implemented) that Rachel talks about in her first paragraph.
If you really care about having a good and reliable product you need people involved with the design and implementation that are deeply invested in making it reliable and maintainable in the long term - which means either making your dev roles shoulder some of the oncall burden or having people that straddle the ops and dev teams. Or both. If you're having difficulty filling this role, perhaps this is the real problem?