ציטירנדיקער פּירוש אויף שמות 2:22

שם האחד גרשם, the name of the one was Gershom, etc. Although the reason Moses named this son Gershom has already been mentioned in Exodus 2,22, it had to be repeated here in order to inform us that we are talking about the same son already mentioned in chapter 2 (though this may have been 60 years earlier) and not another son (by the same name but born of a different mother).

AND HER TWO SONS; OF WHOM THE NAME OF THE ONE WAS GERSHOM. Even though this is not the place where [the narrative of] their birth is told, Scripture here explains the names of the two sons [of Moses — Gershom and Eliezer —] because there was no opportunity to mention the name of Eliezer at his birth, as I have explained in Seder V’eileh Shemoth.⁶¹Above, 4:20. See Ramban there regarding why Eliezer was not named at that time. Gershom’s name, on the other hand, is mentioned in 2:22. Here, Scripture wanted to mention the kindness that the Holy One, blessed be He, had shown to Moses, who was a stranger in a strange land. [When he named his second son], he gave thanks there to G-d for having delivered him from the sword of Pharaoh when he fled from before him,⁶²Ibid., 2:15. [and for making him] now king over Israel, and [because] He drowned Pharaoh and his people in the sea.
The sense of the expression for he said, I have been a stranger, etc. is connected with Moses, who is mentioned in the first verse, [and not with Jethro, who is mentioned in the second verse]. Similarly, the following verse, And the name of the other was Eliezer: for the G-d of my father was my help,⁶³Verse 4. is connected with the expression for he said, [found in the verse before us. It thus reads: “And the name of the other was Eliezer; for he said: for the G-d, etc.”] There are many cases like that.

Furthermore, the Torah may have had to mention that the reason was not that Yitro had expelled Moses from his home. While it is true that Moses said: "I used to be a stranger in a strange country" (obviously not referring to his being expelled by Yitro), he may have phrased it thus so that Yitro should not hear that he had referred to expulsion by him. The Torah repeats here once more that the reason for Gershom's name was Moses' grateful acknowledgement of having prospered as a fugitive in a strange land.