Hello Angwm - we sell into the Philippines through multiple distributors on a private label basis, so I do not know the answer to your first question. The only evidence I have that it should be okay is that the checklist for getting the CPR (certificate of product registration) does not seem to eliminate or address the issue of whether the device is already being imported into the Philippines.
(PDF warning)
https://ww2.fda.gov.ph/attachments/article/95819/Checklist Requirements CPR New.pdf
Regarding your second question, this all revolves around the LTO (License to Operate) of your distributor. When we changed our company name, this impacted our customers/distributors as they had to amend their LTOs and they were not happy. From research on the government websites, it appears that a change in the products being sold by the distributor (including adding or removing) requires an amendment to their LTO. The amendment process of the LTO seems to be that they submit the amendment and it is included in the dossier for their LTO but the changes will not happen until their LTO renews.
So it looks like the process would not be a transfer of the CPR, it would be an amendment to the LTO and issuance of a new CPR to the new distributor. Depending on when the LTO of your existing distributor expires, you could simply refuse to comply with their requests to provide documentation to renew their LTO, in which case they would lose their CPR for your product.
I hope this provides a starting point for your further research.