Yes, you can restore your database backup file (.bak) to a different database by providing a new database name. Further, it is possible to change the Data and Transaction log file location as desired.
Use the following script,
RESTORE DATABASE
MyDB
FROM DISK = '\\MyShare\MyBackup.bak'
WITH
MOVE 'DataFile' TO 'D:\myNewDBLocation\DataFile.mdf',
MOVE 'LogFile' TO 'E:\\myNewDBLocation\LogFile.ldf', REPLACE