The lender will issue the 1098 to the first borrower listed on the mortgage and use the SSN of that borrower.
You can, of course, fill out the loan application with your fiancé as the first borrower but the lender is free to deny you the loan if you don't do it the lender's way.
As for who gets the deduction, the following comes from IRS Publication 936
"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 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 11, and print “See attached” next to the line. Also, deduct your share of any qualified mortgage insurance premiums on Schedule A (Form 1040), line 13.
Similarly, if you are 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 10. Let each of the other borrowers know what his or her share is."
http://www.irs.gov/pub/irs-pdf/p936.pdf
If you get the 1098 and your fiancé takes the deduction for interest and property taxes, attach a duplicate statement to each return explaining the agreement. At least, that way you get it on record. Do it every year.