We have the same issue with some LG and Samsung monitors, they don't report model names.
They do however report correct PNP Device ID's, so what I did was to modify a custom monitor report that was posted on the forums, and them add a column with the PNP Device ID, so I could see all the models on one report.
I grabbed the PNP Device ID's from DriverAgent's Database, 
here
Select Top 1000000 tblAssets.AssetID,
  tblAssets.AssetName,
  tsysAssetTypes.AssetTypeIcon10 As icon,
  tsysOS.OSname,
  LTrim(RTrim(tblMonitor.MonitorManufacturer)) + Case
    When tblMonitor.MonitorManufacturer = 'ACR' Then ' (Acer)'
    When tblMonitor.MonitorManufacturer = 'ACI' Then ' (Asus)'
    When tblMonitor.MonitorManufacturer = 'AUO' Then ' (AU Optronics)'
    When tblMonitor.MonitorManufacturer = 'BA_' Then ' (Barco)'
    When tblMonitor.MonitorManufacturer = 'DEL' Then ' (Dell)'
    When tblMonitor.MonitorManufacturer = 'HWP' Then ' (HP)'
    When tblMonitor.MonitorManufacturer = 'IFS' Then ' (InFocus)'
    When tblMonitor.MonitorManufacturer = 'LEN' Then ' (Lenovo)'
    When tblMonitor.MonitorManufacturer = 'LGD' Then ' (LG)'
    When tblMonitor.MonitorManufacturer = 'LPL' Then ' (LG)'
    When tblMonitor.MonitorManufacturer = 'GSM' Then ' (LG)'
    When tblMonitor.MonitorManufacturer = 'PHL' Then ' (Philips)'
    When tblMonitor.MonitorManufacturer = 'SAM' Then ' (Samsung)'
    When tblMonitor.MonitorManufacturer = 'SEC' Then ' (Samsung)'
    When tblMonitor.MonitorManufacturer = 'TQ_' Then ' (Totoku)'
    When tblMonitor.MonitorManufacturer = '' And Left(tblMonitor.MonitorModel,
    4) = 'IBM ' Then 'IBM' Else '' End As MonitorManufacturer,
  Case When tblMonitor.PNPDeviceID Like '%GSM4B7A%' Then 'W1934'
    When tblMonitor.PNPDeviceID Like '%GSM443C%' Then 'L1718S'
    When tblMonitor.PNPDeviceID Like '%GSM446F%' Then 'L1753S'
    When tblMonitor.PNPDeviceID Like '%GSM4B32%' Then 'L192WS'
    When tblMonitor.PNPDeviceID Like '%GSM4B6A%' Then 'L194W'
    When tblMonitor.PNPDeviceID Like '%GSM4B6F%' Then 'W1942'
    When tblMonitor.PNPDeviceID Like '%GSM4E47%' Then 'L204WT'
    When tblMonitor.PNPDeviceID Like '%GSM43CC%' Then 'L1750S'
    When tblMonitor.PNPDeviceID Like '%SAM02B6%' Then '245B'
    When tblMonitor.PNPDeviceID Like '%SAM03D0%' Then '923NW'
    When tblMonitor.PNPDeviceID Like '%SAM04D3%' Then '2494H'
    Else tblMonitor.PNPDeviceID End Model_PNPDeviceID,
  tblMonitor.MonitorModel,
  tblMonitor.SerialNumber As MonitorSerial,
  Convert(VarChar(10),tblMonitor.ManufacturedDate,120) As ManufacturedDate,
  tblAssets.Domain,
  tblAssets.IPAddress,
  tsysIPLocations.IPLocation,
  tblAssetCustom.Model,
  tblBaseBoard.Product,
  tblAssetCustom.Serialnumber,
  tblAssets.Memory,
  tblAssets.Processor,
  tblAssets.Lastseen
From tblAssets
  Inner Join tblAssetCustom On tblAssets.AssetID = tblAssetCustom.AssetID
  Inner Join tsysAssetTypes On tsysAssetTypes.AssetType = tblAssets.Assettype
  Inner Join tblSystemEnclosure
    On tblAssets.AssetID = tblSystemEnclosure.AssetID
  Inner Join TsysChassisTypes On tblSystemEnclosure.ChassisTypes =
    TsysChassisTypes.Chassistype
  Inner Join tsysIPLocations
    On tblAssets.IPNumeric Between tsysIPLocations.StartIP And
    tsysIPLocations.EndIP
  Inner Join tsysOS On tblAssets.OScode = tsysOS.OScode
  Inner Join tblComputersystem On tblAssets.AssetID = tblComputersystem.AssetID
  Inner Join tblMonitor On tblMonitor.AssetID = tblAssets.AssetID
  Inner Join tblBaseBoard On tblAssets.AssetID = tblBaseBoard.AssetID
Where tblAssetCustom.State = 1