First, Open Exchange management Shell as administrator.

To view list of database in the server : 

Get-MailboxDatabase -Server [Server_Name] [Enter]

or 

Get-MailboxDatabase | Format-List Name, EdbFilePath, LogFolderPath

Change database name :

Set-MailboxDatabase "Current_Database_name" -Name "put_new_name here" [Enter]

Example : 

Rename-MailboxDatabase -Identity "Mailbox Database 1936511020" -NewName "MBDB01"

Change path location of database and log files : 

Move-Database [database_Name] -EdbFilePath [new_path_database] -LogFolderPath [new_path_log]

Example : 

Move-DatabasePath MBDB01 -EdbFilePath D:\MailboxDB\MBDB01\MBDB01.edb -LogFolderPath L:\Logs\MBDB01

To check database identity : 

Get-Mailboxdatabase -Identity [database_name] | fl