LOGNAME and USERNAME are set the same way as USER

doc/sudo.cat

@@ -491,6 +491,12 @@ EENNVVIIRROONNMMEENNTT
                       is enabled in _s_u_d_o_e_r_s and _H_O_M_E is not present in the
                       _e_n_v___k_e_e_p list.
 
+     LOGNAME          Set to the login name of the target user when the --ii
+                      option is specified, when the _s_e_t___l_o_g_n_a_m_e option is
+                      enabled in _s_u_d_o_e_r_s or when the _e_n_v___r_e_s_e_t option is
+                      enabled in _s_u_d_o_e_r_s (unless LOGNAME is present in the
+                      _e_n_v___k_e_e_p list).
+
      PATH             May be overridden by the security policy.
 
      SHELL            Used to determine shell to run with --ss option.
@@ -514,8 +520,9 @@ EENNVVIIRROONNMMEENNTT
 
      SUDO_USER        Set to the login name of the user who invoked sudo.
 
-     USER             Set to the target user (root unless the --uu option is
-                      specified).
+     USER             Set to the same value as LOGNAME, described above.
+
+     USERNAME         Same as USER.
 
      VISUAL           Default editor to use in --ee (sudoedit) mode if
                       SUDO_EDITOR is not set.

doc/sudo.man.in

@@ -997,6 +997,23 @@ is not present in the
 \fIenv_keep\fR
 list.
 .TP 17n
+\fRLOGNAME\fR
+Set to the login name of the target user when the
+\fB\-i\fR
+option is specified, when the
+\fIset_logname\fR
+option is enabled in
+\fIsudoers\fR
+or when the
+\fIenv_reset\fR
+option is enabled in
+\fIsudoers\fR
+(unless
+\fRLOGNAME\fR
+is present in the
+\fIenv_keep\fR
+list).
+.TP 17n
 \fRPATH\fR
 May be overridden by the security policy.
 .TP 17n
@@ -1037,9 +1054,13 @@ Set to the user ID of the user who invoked sudo.
 Set to the login name of the user who invoked sudo.
 .TP 17n
 \fRUSER\fR
-Set to the target user (root unless the
-\fB\-u\fR
-option is specified).
+Set to the same value as
+\fRLOGNAME\fR,
+described above.
+.TP 17n
+\fRUSERNAME\fR
+Same as
+\fRUSER\fR.
 .TP 17n
 \fRVISUAL\fR
 Default editor to use in

doc/sudo.mdoc.in

@@ -926,6 +926,22 @@ and
 is not present in the
 .Em env_keep
 list.
+.It Ev LOGNAME
+Set to the login name of the target user when the
+.Fl i
+option is specified, when the
+.Em set_logname
+option is enabled in
+.Em sudoers
+or when the
+.Em env_reset
+option is enabled in
+.Em sudoers
+(unless
+.Ev LOGNAME
+is present in the
+.Em env_keep
+list).
 .It Ev PATH
 May be overridden by the security policy.
 .It Ev SHELL
@@ -956,9 +972,12 @@ Set to the user ID of the user who invoked sudo.
 .It Ev SUDO_USER
 Set to the login name of the user who invoked sudo.
 .It Ev USER
-Set to the target user (root unless the
-.Fl u
-option is specified).
+Set to the same value as
+.Ev LOGNAME ,
+described above.
+.It Ev USERNAME
+Same as
+.Ev USER .
 .It Ev VISUAL
 Default editor to use in
 .Fl e