Who is listed on the 1098 doesn't really matter. See below.
For info on the mortgage deduction see IRS Publication # 936 -- https://www.irs.gov/pub/irs-pdf/p936.pdf
To claim the deduction you the loan must be secured by your main home or a second home. (You can only have one second home during any year). I would read the section on second homes to be sure this is a second home for you. (Page #4 of pub 936). You must be liable for the debt, which you say you are.
If those are true then Pub 936 page 9 tells you how to report if the 1098 is in one person's name/SSN:
More than one borrower.
If you and at least
one other person (other than your spouse if you
file a joint return) were liable for and paid interest on a mortgage that was for your home, and
the other person received a Form 1098 showing
the interest that was paid during the year, attach a statement to your paper return explaining
this. Show how much of the interest each of you
paid, and give the name and address of the person who received the form. Deduct your share
of the interest on Schedule A (Form 1040),
line 8b, and print “See attached” next to the line.
Also, deduct your share of any qualified mortgage insurance premiums on Schedule A (Form
1040), line 8d.
Similarly, if you're the payer of record on a
mortgage on which there are other borrowers
entitled to a deduction for the interest shown on
the Form 1098 you received, deduct only your
share of the interest on Schedule A (Form
1040), line 8a. Let each of the other borrowers
know what his or her share is.
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