It only cares to the extent that it can analyze which filing status works better. If the income was for just you, select "me". If it was income derived from a joint effort, select "both of us." Ultimately, assuming you file as "Married, Filing Jointly," it won't matter since your incomes will be combined anyhow.

The bank will sometimes only list the first name on a joint account on the 1099.  If the income is for a joint account, you can choose 'both of us'.   It will only matter if you decide to file separately as opposed to jointly.