Steve Jones shows how to rename a primary key constraint:
When you compare that with the same table in another database, what’s the likelihood that you’ll have the PK named PK__OrderDet__D3B9D30C7D677BB4? Probably pretty low.
This means that if you are looking to deploy changes, and perhaps compare the deployment from one database to the next, you’ll think you have different indexes. Most comparison tools will then want to change the index on your target server, which might be using this technique. Or the choice might be something that performs much worse.
What we want to do is get this named the same on all databases. In this case, the easiest thing to do with rename the constraint on all systems. This is easy to do with sp_rename, which is better than dropping and rebuilding the index.
Do read this and avoid renaming a constraint the bad way.