I have a secret stored in Secret Manager, it's for a rds database, is there a way to get the name of this rds database? I couldn't find it anywhere (I can only get a secret name...)Because I wanted to know which vpc is this rds using but I can't find which db is it.... Thanks.
Secrets in Secret Manager don't keep track of which component/application is using them.
You might be able to get this information by looking at the CloudTrail logs if the deployment is recent and you have the service enabled - docs here. By looking at the logs you might be able to at least understand which API calls were made towards SM and which secret was involved.
Based on your question, the reason for you looking for this info is that you'd like to find out the VPC in which your RDS has been deployed. If this is still the case you can do so by identifying the VPC Security Group attached to your RDS Instance. Once you have found the SG you'll have also the id of the VPC in which this SG exists.