The evidence is that ordinary Jews in the first century used the divine name in the form Yaho. It is natural to assume that Jesus used the divine name whenever the occasion arose, unless there is evidence to the contrary. There is no record in the NT that Jesus subscribed to any superstition that the divine name was to be avoided.
And I think there is specific evidence in the gospels that Jesus used the divine name. When Jesus was tempted by Satan in the wilderness he cited three Bible texts that included the divine name. It’s difficult to think this wasn’t deliberate (“the name of Jehovah is a strong tower” Prov 18.10) and equally difficult to believe that having selected texts with the divine name that he then avoided using it.
Matt 4
4 But he answered: “It is written: ‘Man must live, not on bread alone, but on every word that comes from Jehovah’s mouth.’”
7 Jesus said to him: “Again it is written: ‘You must not put Jehovah your God to the test.’”
10 Then Jesus said to him: “Go away, Satan! For it is written: ‘It is Jehovah your God you must worship, and it is to him alone you must render sacred service.’”