Username Variable in custom links?

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The User data of the currently logged in user in WordPress can be retrieved via wpget_current_user()

So you should be able to do something like this in your theme or wherever.

    $current_user = wp_get_current_user();
    echo '<a href="http://example.com/members/' . $current_user->user_login . '/profile">Your profile</a>.';

And build your link that way.

HTH