How are you separating the names in the textbox? You could separate them with commas like this:

Alice Brooks, Charlie Davies, Erica Fletcher, Gordon Haynes

Then you could use something like this (in conjunction with the previous code):

Private Sub Searchbutton_Click()

Dim nameList As Variant
Dim outputList As String
Dim i As Long

nameList = Split(TextBox1.Text, ",")
For i = 0 To UBound(nameList)
    outputList = outputList & "," & GetUserEmailAddress(Trim(nameList(i)))
Next i
TextBox2.Text = Mid(outputList, 2)

End Sub
WBD