If we move a branch, does that new branch location need a new RSSD# or will the old one work since is the same branch just a new location?

You will want to contact your regulator or look it up to see what RSSD# has been assigned (which you can do here: https://www.ffiec.gov/npw). If I recall correctly, I have heard that sometimes it remains the same but it could change.

From CTR FAQ 32:
When the transaction takes place at a branch location, you should include the RSSD number associated with that branch. If the branch location at which the transaction occurred does not have an RSSD number, however, leave all of Item 39 blank. This may occur if an RSSD number has not yet been issued for a new branch, but we expect few depository institutions to not have an RSSD for each branch. If the branch has the same RSSD number as the financial institution as a whole, you should use the overall financial institution RSSD number. This will occur with credit unions.

The RSSD ID is the primary identifier on the database. It is a unique, one-up number (with a check digit) that is assigned by the RSSD software when an entity is first added to the database. This identifier has no inherent attribute information, never changes, and is never reused. Each entity has one and only one ID_RSSD during its life cycle; this is essential for tracing an entity's existence and relationships and linking it to financial data.

While the entity may undergo major changes, for example, of charter type or establishment type, it will continue to have the same ID_RSSD. An entity ceases to exist when it is liquidated or permanently closed. Even after its existence is completely terminated, it will remain on the database with the same ID_RSSD.