Applying for disability and actually getting it are 2 different things. Most cases are denied at first. The national average of initial denials is about 66%: https://www.ssa.gov/policy/docs/statcomps/di_asr/2011/sect04.html
Most people then get an attorney and appeal. However, the time to see a judge about the denial can be very long, in Phoenix, AZ looks to be about 17 months: https://www.ssa.gov/appeals/DataSets/01_NetStat_Report.html
And there is no guarantee he will end up winning his case. If it is for a psych disability, be aware that those cases are very difficult to prove.
Also, if you and your husband get support from his family or live with them, or if you decide to become employed, his disability payments can be substantially reduced. https://az.db101.org/az/programs/income_support/ssi/program2a.htm
Therefore, the co-sponsor's assets will be the most important.
You only need to include other legal names, no nicknames.
For example, if you had changed your name before due to a previous marriage, you would include your maiden name and your married name, even if you changed back to your maiden name after a divorce.
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