Don't change the name of column. Try this
DataGridView1(DataGridView1.Columns("Edit").Index,DataGridView1.CurrentCell.RowIndex).Value = "Save"
You need to change your conditions accordingly, I mean, based on
Value
.
[Edit]
It should go like this.
If dgv(dgv.Columns("Edit").Index, dgv.CurrentCell.RowIndex).Value = "Edit" Then
dgv(dgv.Columns("Edit").Index, dgv.CurrentCell.RowIndex).Value = "Save"
Else
dgv(dgv.Columns("Edit").Index, dgv.CurrentCell.RowIndex).Value = "Edit"
End If