1. Most English translations translate the first word of the sentence weha'adam as '[Now] Adam.' The Hebrew word has the definitie article, and should properly be translated as "the man" (as in NASB & NRS) though "Adam" is certainly meant. The name proper noun 'adam appears in v25.
2. While "the meaning of the name-giving as a whole is clear" (C. Westermann), the Hebrew sentence is difficult. "With the help of Yahweh" is 'et-YHWH. But 'et- is never used anywhere else in the Hebrew Bible to mean "with the help of." 'et is a very common word in the OT, and is used either as a direct object marker (indicating that the noun that follows it is the direct object of the verb in the sentence, and, therefore, usually left un-translated; besides, there is no direct equivalent in the English language) or as a preposition meaning 'with.' For a summary of the discussion about resolving this difficulty, see C. Westermann, Genesis 1-11 A Commentary (Minneapolis: Augsburg Publishing House, 1984):289-92. It is equally mystifying why Eve would speak of her infant as an 'ish, which in Hebrew normally refers to a grown male person.