roggie

The WordPress “Meta” widget uses a lot of screen space and presents more information than some site designers would like. The Login/Logout plugin provides web designers with a compact alternative.
Available translations: English, French, German, Italian, Spanish, Catalan, Dutch, Polish, Norwegian and Persian.
The plugin can be used as a widget in themes that include sidebars. Alternatively, it can be added to your site’s footer or any other part of the site by inserting “rh_hype_lilo(); into your site’s PHP.
When the user is not logged in, the plugin presents a link so the user can Login, and an option allows another link to Register. Once logged in, users are redirected back to the page they came from. The plugin also displays the username and has an option to also display their email address.
There is also a link to Logout and, depending on the user’s role, a link to their profile or to the main site administration pages. Users are redirected back to the page they came from after they logout.
When used as a widget, a hyperlink option enables the widget to display an arbitrary number of hyperlinks to other sites/pages. These links are displayed only to logged in users. Other options enable the appearance of the widget to be customized to suit the theme design.
You must logout and in again to see changes such as new links etc. in the widget.
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Login-Logout

Adds simple, clean links so users can login/logout & register easily. Highly customisable, & can be used as a widget or inserted into your sit …

Julio Potier

Grégory Viguier

SecuPress

This plugin forbids access to https://example.com/wp-login.php and creates new urls, like https://example.com/login or https://example.com/logout. 
This is a great way to limit bots trying to brute-force your login (trying to guess your login and password). Of course, the new URLs are easier to remember too.
Also remember: the use of this plugin does NOT exempt you to use a strong password. Moreover, never use “admin” as login, this is the first attempt for bots.
By the way, if you are looking for a complete security solution, take a look at <a href="https://wordpress.org/plugins/secupress/" rel="ugc">SecuPress</a>: Move Login is included inside.
<h4>Multisite</h4>
Yes! The plugin must be activated from your network. 
Note 1: this plugin deals only with <code>wp-login.php</code>, not with <code>wp-signup.php</code> nor with <code>wp-activate.php</code> (yet). That means https://example.com/register will still redirect to https://example.com/wp-signup.php. I think this will be the next step though, but no ETA. 
Note 2: if users/sites registrations are open, you shouldn’t use this plugin yet. There are some places where the log in address is hard coded and not filterable. A <a href="https://core.trac.wordpress.org/ticket/31495" title="Always use 'login' as $scheme parameter for "login-ish" URLs, and other inconsistencies" rel="nofollow ugc">bug ticket</a> is open.
<h4>Requirements</h4>
<ul>
<li>You will need a FTP access: if the <code>.htaccess</code>/<code>web.config</code> file is not writable (you will need to add the given rules manually), or if something is wrong and you can’t log in anymore (see the FAQ in that case).</li>
<li>Should work on IIS7+ servers but not tested (I guess you should probably save a copy of your <code>web.config</code> file before the plugin activation).</li>
<li>For Nginx servers, the rewrite rules are not written automatically of course, but they are provided as information in the plugin settings page.</li>
</ul>

Move Login

Don't know why I didn't find "Move Login" first. I already tested 2 alternative free plugins and it was deficient in different ways.  "Move Login" is powerful, light and easy to set up. Very nice find. Thanks.

The best of the 3 ones I tested

Change your login URL for something like https://example.com/login and stop login brute-force attempts.

Login-Logout vs Move Login