Letters of Loftiness
R' Simcha ben R' Gershon Hakohen¹ teaches that initially they were called Dovid and Yonasan. But after Dovid swore to Yonasan, Hashem's name of י-ה was added to their names. Dovid was given the yud making his name דויד and Yonasan had a hey added making it יהונתן.
In this way we can explain: נפלאתה אהבתך לי ², מאהבת נשים your love was more wonderful to me than the love of women: just like a man and woman who merits, the name of Hashem י-ה is placed upon them,³ so too, Dovid and Yonasan merited and had added to their names Hashem's י-ה.
¹ In his sefer Sheimos p 43a.
² Shmuel 2, 1:26.
³ Sota 17a. The name of Hashem, י-ה, is found in the words איש and אשה, representing Hashem's presence. If they do not merit, then Hashem withdraws His name from among them, leaving אש and אשה, where the marriage is consumed by the fires of domestic discord.