I don't know the names. but this looks like your basic Val.
actually, this looks a little more like Dwarf Sagittaria. This is normally sold as a carpeting plant. depending on the over all parameters this plants can carpet like mad staying small. Or it can grow up and become more like Vallisneria. But this should only grow to about 8 maybe 10 inches max. This, like Val, will send out runners to the side and create more. So if you leave this your jungle will get larger. Well thicker, maybe not taller.
Below are Dwarf Sag. well the upper left is a poor example as it's a narrow type... but you get it.
I'm not sure what it is, but it's one of the two. Val is the same as the Dwarf Sag as far as color and duplication process, but it will get up to 4' long if you let it/it's able.
To tell as time goes on:
Val will get taller, all the way to the tank surface. It will spread too but it will grow up more than out.
DS will likely not get any taller than it is now and after about 3-6 weeks I would suspect the root structure will have come in well enough for it to start to spread and it will do this quicker and quicker once it starts.
Now that I have said all that and looked at your photos a couple times, my bet is that it is just the regular Valisneria, the most common types. Again will get tall and then spread out, You will have to trim it from time to time as it will grow taller than your tank can go and it will create a canopy if you let it.
Edit: there is a Sagittaria Subulata that is a larger version of Dwarf Sagittaria that I have been talking about. Could be this, likely only up to 8-10". So again, in time you will know for sure.