юзер

Private Declare Function GetUserName Lib "advapi32.dll" Alias _
"GetUserNameA" (ByVal lpBuffer As String, _
nSize As Long) As Long

Private Sub UsrName1()
Dim strUserName As String
strUserName = String(100, Chr$(0))
GetUserName strUserName, 100
strUserName = Left$(strUserName, InStr(strUserName, Chr$(0)) - 1)
MsgBox strUserName
End Sub

компьютер

Private Const MAX_COMPUTERNAME_LENGTH As Long = 31
Private Declare Function GetComputerName Lib "kernel32" Alias _
"GetComputerNameA" (ByVal lpBuffer As String, nSize As Long) As Long

Private Sub CompName()
Dim dwLen As Long
Dim sString As String
dwLen = MAX_COMPUTERNAME_LENGTH + 1
sString = String(dwLen, "X")
GetComputerName sString, dwLen
sString = Left(sString, dwLen)
MsgBox sString
End Sub