Not necessary, but, for the sake of continuity I usually buy the same brand of primer and paint. The chemistry of paint is such nowadays that each company has a "system" which makes the paint finish a better product in the end if you stay with the same co. But, like I said, it's not necessary. I have used Valspar primer and SW for walls and had no issues.
If you are going from a glossy oil to a latex........scuff sand and use a bonding primer first before applying the finish coats. Those oils can be so glossy that you get "fish eyes" in your finish and bonding issues if you don't use a bonding primer such as Zinsser's 1-2-3.
If you do not mind working with a solvent based primer, and assuming you can buy it where you live, I still like going with an alkyd primer/underlay over oil finish and then putting on two coats of a nice acrylic finish of quality.
A bonding latex primer will work though. As mentioned, you must scruff up the surface with fine grit paper so the primer will stick. You will want to wash the surfaces if the oil product has chalked.