I believe the correct answer, given already, is that using the servant's name adds substance and credibility to the account.
Theophylact, who synopsized the various Patristic commentaries on the Gospels, writes:
The miracle was so astounding that the Evangelist provides the name of the servant: if a reader of his Gospel doubted, he could investigate for himself and verify the facts.1
John Chrysostom, for example, wrote in the late 3rd/early 4th century:
The Evangelist adds the name of the servant, because the thing done was very great, not only because He healed him, but because He healed one who had come against Him, and who shortly after would buffet Him, and because He stayed the war which was like to have been kindled from this circumstance against the disciples. For this cause the Evangelist hath put the name, so that the men of that time might search and enquire diligently whether these things had really come to pass.2
1. The Explanation of the Gospel of John (tr. from Greek; Chrysostom Press, 2007), pp.269-270.
2. Homily LXXXIII on John (tr. from Greek)