tarppa

Write all login attempts where both username and password are supplied to a log file. The logfile is relative 
to error.log and is called ‘login.log’, the format : “TIMESTAMP USERNAME SUCCESS/FAILURE”.
In practice this plugin is a rewritten version of the wp_authenticate_username_password function from user.php and replaces 
it in the login process.

WP Login Logging

Write all login attempts to a logfile by replacing default wp_authenticate_username_password functionality

Pierre Lannoy

Hosterra

Capture and log events, metrics and traces on your site. Make WordPress observable – finally!
De-facto standard stack for WordPress observability, DecaLog provides reliable and powerful logging, monitoring and tracing features for WordPress core, PHP, database, plugins and themes.
DecaLog captures events generated by WordPress core, PHP, database, plugins and themes, collates metrics and KPIs and follows traces of the full WordPress execution. It has the ability to enrich these events, metrics and traces with many details regarding their triggering, before storing them in WordPress database or passing them to external services.
If you don’t want to use external services, DecaLog provides the tools to leverage all the benefits of observability right in the WordPress admin dashboard. It supports multisite logs delegation and contains many features to help to protect personal information (user pseudonymization, IP obfuscation, etc.).
For a full list of supported – internal or third-party – services please, jump to the official <a href="https://perfops.one/decalog#services" rel="nofollow ugc">supported services list</a>.
DecaLog can be used in dev/debug phases or on production sites: it has nearly no resource impact on the server. It provides an extensive set of WP-CLI commands to help operations too.
<blockquote>
DecaLog is part of <a href="https://perfops.one/" rel="nofollow ugc">PerfOps One</a>, a suite of free and open source WordPress plugins dedicated to observability and operations performance.
</blockquote>
<h4>Developers</h4>
If you’re a plugins / themes developer and want to take advantage of the logging features of DecaLog, there’s a <a href="https://decalog.io/" rel="nofollow ugc">DecaLog SDK</a> for you.
<h4>Support</h4>
This plugin is free and provided without warranty of any kind. Use it at your own risk, I’m not responsible for any improper use of this plugin, nor for any damage it might cause to your site. Always backup all your data before installing a new plugin.
Anyway, I’ll be glad to help you if you encounter issues when using this plugin. Just use the support section of this plugin page.
<h4>Privacy</h4>
This plugin, as any piece of software, is neither compliant nor non-compliant with privacy laws and regulations. It is your responsibility to use it – by activating the corresponding options or services – with respect for the personal data of your users and applicable laws.
This plugin doesn’t set any cookie in the user’s browser.
This plugin may handle personally identifiable information (PII). If the GDPR or CCPA or similar regulation applies to your case, you must use the anonymization options embedded in the plugin and/or adapt your processes (consent management, security measure, treatment register, etc.).
<h4>Donation</h4>
If you like this plugin or find it useful and want to thank me for the work done, please consider making a donation to <a href="https://www.laquadrature.net/en" rel="nofollow ugc">La Quadrature Du Net</a> or the <a href="https://www.eff.org/" rel="nofollow ugc">Electronic Frontier Foundation</a> which are advocacy groups defending the rights and freedoms of citizens on the Internet. By supporting them, you help the daily actions they perform to defend our fundamental freedoms!

DecaLog

Very nice to be able to push certain events to New Relic logs. I can even see Wordfence alerts and user logins coming in which is awesome! 

Great plugin!

Capture and log events, metrics and traces on your site. Make WordPress observable - finally!

WP Login Logging vs DecaLog