As far as I know, the db_name initialization parameter under Oracle Linux and Unix is case sensitive. And I think this is also important for the listener and tnsnames configuration.
Does this also affect the database name or SID in the file system directories like /u01/app/oracle/admin/orcl1/adump?
Prior to 11g and 12c the db_name and ORACL_SID used to be uppercase. However, in recent 11g and 12c installations the defaults seem to be lowercase.
If I look at my current 12c installation, I see the following:
$ ls /u01/app/oracle/admin
+ASM cdb1 cdb2 orcl orcl2 ORCL2 orcl3
$ ls -l orcl2
drwxr-xr-x 2 oracle oinstall 12288 Oct 13 03:58 adump
drwxr-xr-x 2 oracle dba 4096 Oct 13 02:47 xdb_wallet
$ ls -l ORCL2
total 4
drwxr-xr-x 2 oracle dba 4096 Oct 13 03:24 xdb_wallet
I don't know how I ended up with upper and lowercase orcl2, but I was wondering if somebody can confirm whether db_name in lower or uppercase also matters for file directory names.