I don't know how much that can help. If you get called for an interview, then you can show the documents related to the purchase and it may show that OK these guys are serious about living with each other and are making long term decisions(would show more of this if both your names were on it) but if you don't get called for an interview I don't know if USCIS will look at your current financials and obviously even if you have paperwork proving the purchase you won't be able to send it in now because your case is already filed. It would have mattered even more if you had owned it before you filed and had paid some taxes on it. It would, however, definitely add something to your citizenship case whenever you are planning to file that. Secondly, since it’s such an important decision, I don’t know if you want to show them that it has only your name on it. That may raise the question as to: “Why is he only putting his name on it?” It’s again, another way to look at things. If it had only her name on it I am sure USCIS would say oh he really loves her he is buying her an apartment/house but having your name on might make it look bad than good. All in all, I think it can’t really hurt with a possibility of helping you out in the future.