Is rsync is a good choice for my project ?

I have to :
- copy files from source to destination folder via SSH,
- be sure all files are copied,
- delete source files after copy.
- if I have conflict name, I have to rename files.

It looks like I can use option : --remove-source-files (to delete source files)
But how rsync manage conflict, can I had rules ?

Use case on my project :

I run scientific calculation on server A and results are inserted in folder "process", for each calculation I have a repository like this : /process/calc1.
Now I would like to transfer repository "/calc1" to server B (I get /process/calc1), and delete "calc1" from server A.
...During another calculation I get "/process/calc2" on server A, the idea is also to move "calc2" in "/process/" directory on server B, then I have now on server B :
- /process/calc1
- /process/calc2
(and /process/ on server A is empty).

How rsync will manage conflict (on server B) if I have another folder like "/process/calc1" in server A after a new calculation (if "/process/calc1" already exist on server B) ?

Is it possible to add rules with rsync, and rename "/process/calc1" by "process/calc1R2" in server B ? And so on (ex:calc1R3) ?

Thanks.