In 18:3-4 the Torah tells us about Moshe's two children. It says, "אשר שם האחד גרשם כי אמר... ושם האחד אליעזר כי אלקי אבי"
Why by Gershom does it say "And ones name was Gershom because he said..." while by Eliezer it says his "name was Eliezer because God saved us.." why not "because he said" by Eliezer as well?
There is a difference between perspective and fact.
By Gershom's birth, Moshe felt like an outsider. he felt like a stranger in a strange land. Even if he had received citizenship and had been there for a long time and was not considered a stranger, he still felt like a stranger. So he named his child Gershom because he said he was a stranger in a strange land. It was based on his perspective.
When he named Eliezer, it was based on fact, not perspective. Moshe said, I was n danger and Hashem saved me. So he named his kid Eliezer. It was not a matter of perspective, so it is not his viewpoint that is the basis for the name.