The dimension value that is displayed can be replaced using the TextOverride property. Using this property you can completely replace the displayed value of the dimension, or you can append text to the value.
This example appends some text to the value so that both the string and the dimension value are displayed.
Dim dimObj As AcadDimAligned
Dim point1(0 To 2) As Double
Dim point2(0 To 2) As Double
Dim location(0 To 2) As Double
' Define the dimension
point1(0) = 5#: point1(1) = 3#: point1(2) = 0#
point2(0) = 10#: point2(1) = 3#: point2(2) = 0#
location(0) = 7.5: location(1) = 5#: location(2) = 0#
' Create an aligned dimension object in model space
Set dimObj = ThisDrawing.ModelSpace. _
AddDimAligned(point1, point2, location)
' Change the text string for the dimension
dimObj.TextOverride = "The value is <>"