What you heard is correct.Sree is from siri, siri means wealth,and Goddess Laximi is known as the Goddess of wealth.and ja means son/daughter.Sreeja means Son/Daughter of Laximi.The name Sreeja is selected by the parents so as to the child should be wealthy.
Mind one more thing,when ever you find "ja",remember it, Ja means Son/daughter.
Padmaja=born to padma(lotus)
Neeraja=Born in water
Shailaja=Born through stone (shila)(Ahalya=Ahalya was as stone,due to a "shap" of some muni,when Sri Ram's eet touches the stone turns to Ahalya
Himaja=Born in ice(Parwati)
Thanks for asking a good question,and utilising the Y.A. in correct sense ,and I am happy to answer a good question after a long time.Keep it up,and ask if you got any doubt,if I am able to answer I will or some other will answer it definitely,some rude answers may also receive ,just ignore them.
Best of luck.
@Yes,What Mr.Manish has said about Shailaja.Of course in sense of turning,coming for easy understand I said "born to " shila/stone,to understand "Ja".Thanks for correction to Mr.Manish.I welcome you.