If you have not included schema information in your changeSets, everything will work just fine in a different schema. Liquibase tracks the id/author/filename of changesets that have been ran in the databasechangelog table in the user’s default schema (normally). You can change the schema it expects the table to be in with a parameter at runtime if necessary, but you probably do not need to.
If you have included the old schema name in the changeSets, you will want to update them with the correct schema so future database rebuilds will put everything in the correct schema. That will cause your checksums to change and so you will want to use the tag or update the databasechangelog table setting the md5sum column to null so it will recompute the checksums at the next execution time.