John 1:37

And the two disciples heard him speak, and they followed Jesus. And Jesus turned, and beheld them following, and saith unto them, What seek ye? And they said unto him, Rabbi (which is to say, being interpreted, Teacher), where abidest thou?

With reference to the identity of these two disciples, the words of Hovey are logical. One of them, of course, was Andrew, as revealed in John 1:40. Hovey said:

But who was the unnamed companion of Andrew? Probably the Evangelist himself. For: (1) the narrative in this place is very particular and graphic, making it probable that the writer was an eye-witness. (2) The writer of such a narrative would have been sure to mention the name of the other disciple, unless there had been some reason for withholding it. (3) The writer of this Gospel never refers to himself by name, and the same feeling which led him to withhold his name elsewhere accounts for his withholding it here.[41]

What seek ye? ... was an appropriate response by Jesus to the fact of their following him; but their response was more timid and hesitant than we might have expected. Instead of declaring flatly that "We understand that you are the Messiah and would like to follow you," they politely addressed him as "Rabbi," and inquired where he lived! John's explanation of the term "Rabbi" indicates that the greater part of the Christian world to whom this was written was Gentile. The hardening of Israel, as prophesied by Jesus and discussed in the writings of Paul, had long ago occurred; and thus the "Jews," as referred to in this Gospel, are to be identified as the unbelieving and antagonistic portion of Israel.

Rabbi ... By the use of this title, and by their inquiry as to where the Master lived, the two disciples clearly indicated a desire to know more of that Person of whom their beloved teacher had made such amazing statements. The Lord rewarded their interest and desire by his encouragement.