。
She slowly repeated her name.
Literal
She [topic-は] her own name [object-を] slowly [adverbial-と] repeated.
ゆっくりと is the adverbial form of the 擬態語 ゆっくり ('slowly, leisurely, unhurriedly'); the optional と here is the adverbial と that frequently attaches to mimetics and reduplicated adverbs. ゆっくり繰り返した (without と) would be equally grammatical but slightly less rhythmic. 自分の名前 frames the name as 'her own,' implying she was repeating her own name — perhaps to fix it in someone's mind or to make sure it was heard correctly.