First, you need to understand that Dark Matter and Dark Energy are very different things. You should start by reading the Wikipedia article linked to get some general idea of what you’re asking about!
The final component, dark energy, is an intrinsic property of space, and so has a constant energy density regardless of the volume under consideration
So, Dark Energy will not be “more concentrated” near a planet. That's just a non sequitur.
Dark Matter will clump on the scale of galaxies, not a small region within a solar system. Now cutting edge research indicates that there are different kinds of Dark Matter: some is completely non-interacting, and some may interact (and thus condense) a little. So, it may be conceivable that you could get a cloud of DM that’s a “small” clump within a galaxy.
A planet in a system embedded in this cloud would notice nothing. The density is still very low, and it's all around so the gravity cancels out.
Suppose you were to handwave a cloud of DM that’s only millions of miles across, and condensed onto a planet. As far as the rest of the solar system in concerned, that planet would be more massive. You notice the difference when looking at it and seeing that the normal matter seems to be some smaller amount.
This would be very subtle and not immediately apparent in terms of other planet’s interactions. But the moons of that planet — that you would notice. The distant moons would orbit fast, and possibly more distant than the apparently small planet would permit. It would point to a strange excess of mass. Closer moons, those within the DM cloud, would not obey Kepler’s third law! Looking at each moon, you would deduce different values for the mass of the planet! This would certainly confuse the explorers!
The planet would not rotate faster because of it. The surface gravity would be close to normal! You are inside most of the cloud, so only the DM that’s actually inside the planet will add to the surface gravity. You won’t notice this because the effect is small and you can just suppose the rock is of a slightly heavier type, deep inside the world.