The name Rādhā is derived from this verse (S.B.10:30:28), from the words anayārādhitaḥ, meaning "by Her the Lord is worshiped." Sometimes the critics of Śrīmad-Bhāgavatam find it difficult to find Rādhārāṇī’s holy name in that book, but the secret is disclosed here in the word ārādhita, from which the name Rādhā has come. Of course, the name of Rādhārāṇī is directly mentioned in other Purāṇas. This gopī’s worship of Kṛṣṇa is topmost, and therefore Her name is Rādhā, or "the topmost worshiper."
(Sri Caitanya Caritamrta------2:8:100------purport).

In fact, Rādhārāṇī is the internal potency of Śrī Kṛṣṇa, and She eternally intensifies the pleasure of Śrī Kṛṣṇa. Impersonalists cannot understand this without the help of a mahā-bhāgavata devotee. The very name "Rādhā" suggests that Śrīmatī Rādhārāṇī is eternally the topmost mistress of the comforts of Śrī Kṛṣṇa. As such, She is the medium transmitting the living entities' service to Śrī Kṛṣṇa. Devotees in Vṛndāvana therefore seek the mercy of Śrīmatī Rādhārāṇī in order to be recognized as loving servitors of Śrī Kṛṣṇa.
(Sri Caitanya Caritamrta------1:4:56------purport).

The name "Rādhā" is derived from the root word ārādhana, which means "worship." The personality who excels all in worshiping Kṛṣṇa may therefore be called Rādhikā, the greatest servitor.
(Sri Caitanya Caritamrta------1:4:87------purport).