Automated rendering of After Effects or similar
After Effects can be automated using the Adobe extendscript scripting language,  and can be run from the command line, meaning that it can be integrated into other processes.

Extendscript is JavaScript and it works across Adobe's product line (to varying degrees, you can use it to script Photoshop for instance). If you have a JavaScript developer available then this would be a relatively straightforward task.

There are also third party frameworks such as Dataclay that make the process easier for non-technical users to avoid scripting, but they are relatively pricey, though they might work out cheaper than hiring a developer and rolling your own.