The Logical Name field in question, is in:
Database properties->Files

USE [HEALTHCARENEW];
-- Changing Physical names and paths
-- Replace all NewMyDB with the new name you want to set for the DB
-- Replace 'C:\...\NewMyDB.mdf' with full path of new DB file to be used
ALTER DATABASE HEALTHCARENEW MODIFY FILE (NAME = 'HEALTHCARE', FILENAME = 'C:\SQL Database\CSHEALTHCARE.mdf');
-- Replace 'C:\...\NewMyDB_log.ldf' with full path of new DB log file to be used
ALTER DATABASE HEALTHCARENEW MODIFY FILE (NAME = 'HEALTHCARE_log', FILENAME = 'C:\SQL Database\CSHEALTHCARE_log.ldf');
-- Changing logical names
ALTER DATABASE HEALTHCARENEW MODIFY FILE (NAME = HEALTHCARE, NEWNAME = CSHEALTHCARE);

ALTER DATABASE HEALTHCARENEW MODIFY FILE (NAME = HEALTHCARE_log, NEWNAME = CSHEALTHCARE_log);

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