My partner wants me to sign my name off deed but I'm still named on the mortgage. I'm not named on the note.
What are the consequences of being named on mortgage but not on the deed?

The deed is proof of ownership. The mortgage note is proof that you are responsible for paying back the loan. The mortgage is you giving permission to the lender to take the property if you fail to make the payments on the note.

If you take your name off the deed you are giving up your share of ownership of the property. If your name is not on the note then you are not responsible for paying the loan. So leaving your name on the mortgage really has no effect on you at all. If you are married to your partner then some lenders require that the spouse sign the mortgage anyway, even if they are not listed as an owner on the deed, because some states recognize that spouses have some right to ownership of the house in the event of death or divorce. This way if the partner whose name is still on the deed fails to make the payments then the lender can foreclose without having to fight over the spouse's possible rights of ownership.

Please do not consider taking your name off the deed until you have discussed it with an attorney. By doing so you will be giving up all of your rights of ownership of the property.