Imagine a spacecraft in a highly eccentric orbit. Say the craft burns at periapsis towards the planet such that its orbital eccentricity does not change and the craft's periapsis moves with the ship so the two stay at the same point at all times. This would result in a circular orbit, but a faster orbit than would normally occur at such an attitude.
Aside from this being horribly wasteful and generally impractical:
My first question is whether this maneuver has a name. I would guess not because it's an extremely wasteful maneuver in most cases, and wouldn't be worth any benefit you could get by performing it.
One possible use case, however improbable the scenario, would be to accelerate an orbit. Imagine a spacecraft in low-earth orbit moving at 7.5km/s. If the craft were to burn prograde until it were moving at 15km/s (doubling its velocity) and then continuously burn towards the planet as I described, it could effectively halve its orbital period by doubling the centripetal force keeping the craft in orbit (half of the acceleration is due to gravity, half due to the constant burn).
Is there a more efficient way than this to accelerate your orbit beyond the orbital rate that can be achieved just above the Carmen line (assuming we don't want to drop below the line)?