I painted wood with Valspar satin finish paint, but I don't like the texture because it is rough. I was wondering if I can paint over it with a second coat of a different brand, colour matched and the same finish?
Technically yes as long as it is the same base (assuming your existing valspar paint was latex, you would need another latex paint).
The sheen or finish of your paint (flat/satin/semi/gloss) is of no concern and shouldn't provide a problem.
However, doing so likely won't do what you want. Assuming your dissatisfaction in texture is more than simply the difference between flat/gloss paint, it means the surface you painted was likely the source of your roughness. You need to smooth (sand) the surface before painting.
Coming from the Paint Department at Lowe's and serving at two different stores two different paint departments and working with several Valspar reps I can firstly tell you that Valspar does in fact carry Oil-Based paints. They just may not be available at every Lowe's near you.
You can definitely do this. There is actually no harm in doing this at all. Think of it this way. Just imagine you move into a new house and the rooms are already painted. They chose an eggshell finish. You get in there and prefer semi-gloss finish. You like the color, so you pull a chip and get it color matched. The same scenario is what you're facing here. The only difference is YOU painted the first coat.
This is a very common scenario and I'm not sure what the other answers are referring to in regards to not doing what you want. If you want a different sheen, go ahead and apply that coat of paint over it. Make sure it's even and the desired effect will be just as expected and nothing less.
Same base, different base it doesn't matter. Paint is plastic. It doesn't matter if you had flat paint on originally and wanted to cover it with enamel. The only thing I would recommend is using Valspar's primer paint. I believe it's newer to the Valspar lines and they have several options for you.
Now you mention that you want to use a different brand of paint. This should be fine, in general. Valspar is a very thick paint, and I'm not sure that you can get the same one-coat coverage of say a cheaper paint like Olympic, but the Olympic Primer Paint is good stuff also.
The texture is going to be as rough as the surface you're applying it to. You should've sanded down the wood somewhat smooth, primed the wood, and then used a paint over that. Preparation is 80% of painting.
Hope this helps!