Looks like all you need is to use the Find method - something like this
(not verified). FIND is Very powerful - I usually use function that
receives the sheet  and string as parameters but it is not necessary.

With ws 'Your Worksheet where the row will be deleted

Set rFind = Columns(2).Find(What:= TextName.Text,
LookIn:=xlValues, _ LookAt:=xlWhole, SearchOrder:=xlByRows,
SearchDirection:=xlNext, MatchCase:=False, SearchFormat:=False)

' delete  Selected ROW from Worksheet

rFind.Row.EntireRow.Delete

end with