While I have not read Anne Sullivan's original text nor a biography of Keller, and I cannot say for sure what was happening in her head, here is one plausible theory:

For the longest time, despite learning many words for use in daily life, Keller did not actually grasp the concept of words being names of specific objects; rather, she regarded them as combinations of letters loosely associated with specific situations and sensations. For example, "mug" and "milk" and "drink", as far as she was concerned, were all just arbitrary combinations of signs that her teacher tended to utter in association with drinking milk. In this view, when describing Helen's prior attitude as follows:

This morning, while she was washing, she wanted to know the name for “water.” When she wants to know the name for anything, she points to it and pats my hand

the teacher, Sullivan, is not actually speaking precisely: at that time, Keller did not actually want to know the 'name' of the object 'water'; she wanted to know 'what kind of letter combination is associated with the experience of washing'.

Once again, this is just the way in which I understand it, and I'm not saying this is actually the way Helen Keller thought.