I would do 1 or 2 if the DO offers it. I believe some offices don't do name change, period. For example San Jose I don't think they do name changes. At least they didn't a few years ago. If you change name after naturalization you'll have to use your old certificate with your new court papers to obtain passport and things like that. If you do it before or during naturalization you'll end up with a certificate with your changed name that you can use for obtaining passport and any other document under your new name. I wouldn't be scared about any delays because of checking your old name, it probably won't have any impact. Go ahead and change name ahead of naturalization or during naturalization if your office entertains the idea of judicial naturalization.
N-400 timeline
DO : San Jose
11/28/2006 : Mailed
12/04/2006 : PD (and Receive Date)
12/05/2006 : Check cashed
12/11/2006 : Notice Date (Received on the 14th)
12/22/2006 : FP ND
01/09/2007 : FP Appt
12/29/2006 : FP Done. Walk-In
07/17/2007 : Interview (ND May 17)
08/22/2007 : Oath (Received Jul 26, issued on the 23d, mailed on 24th)
08/23/2007 : Applied N-600 and Expedited Passport
09/06/2007 : Passport received
08/20/2008 : Sent N-565 (Approved Feb 17, 2009)
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