A certified diver is a diver. You should be able to dive to your experience level whatever the affiliation of the dive shop.
But if you are doing a "referral" you should if possible choose a dive center for the dives with the same affiliation as that where you do your earlier training. If it's PADI you can go to www.padi.com
to see which dive centers are approved. For the four dives for the PADI Open Water certification we charge US$225.
It is possible to complete the dives under a different training body from that you started with, and you will be able to choose which body certifies you. But you will need to have completed all the requirements of the body that certifies you, which may entail some additional work. I'll expand on this if anyone wants me to.