。
She seemed to have completely forgotten my name.
Literal
She [topic-は] my name [object-を] forgot [completely-てしまっている] [seemed-ようだった].
An impressive stack of auxiliaries. 忘れて + しまって + いる + ようだった layers four meanings: (1) the te-form of 忘れる ('forget') feeds (2) ~てしまう ('completely / regrettably,' here marking the forgetting as complete and unfortunate), then (3) ~ている marks the resulting state ('is in the state of having forgotten'), and finally (4) ~ようだった is the past evidential ('seemed to'). Each layer adds nuance without breaking syntax — Japanese auxiliary stacking is one of the language's more intricate features. The whole sentence reads as a delicate observation of past appearance.