It certainly should generate the keyfile to the .ssh
subdirectory of your home directory, at least if you just hit return to accept the default when it asks you for a location for the keyfile; here's a copy/paste of a shell in a newly-created account where it looks like it's working OK:
16:17 ~ $ ssh-keygen
Generating public/private rsa key pair.
Enter file in which to save the key (/home/gt20180330a/.ssh/id_rsa):
Created directory '/home/gt20180330a/.ssh'.
Enter passphrase (empty for no passphrase):
Enter same passphrase again:
Your identification has been saved in /home/gt20180330a/.ssh/id_rsa.
Your public key has been saved in /home/gt20180330a/.ssh/id_rsa.pub.
The key fingerprint is:
79:a0:5c:6b:19:94:a4:30:af:f4:f0:1b:ce:e3:1b:54 gt20180330a@glenn-liveconsole3
The key's randomart image is:
+--[ RSA 2048]----+
| o .o. |
| + o. |
| o o E |
| . * + * |
| . B S . |
| + + . |
| * |
| . o |
| o. |
+-----------------+
16:17 ~ $ ls /home/gt20180330a/.ssh/
id_rsa id_rsa.pub
16:17 ~ $
Is there anything different in your console (apart from the username, of course)?