Let's say there are two people on a bank account. They both file taxes independently and aren't married or anything. Who then pays the taxes for the 1099-INT? Can the payments be split 50/50? Should both parties pay 100% of the 1099-INT taxes?
Generally, the person listed "first" on the account is the person considered to receive the interest on the account, and is the one that the bank issues the 1099-INT to. (See "SSN for joint account" in Publication 550.) For more specific details about your account, you could contact the bank and they could let you know which person is the "primary" person. If you do nothing else, and this arrangement is acceptable to the owners, that person will include the interest in his or her income, and the other owner (or owners) on the account won't need to do anything about it.
If you want to allocate the interest differently for tax purposes (such as your proposal that you want to split the income 50/50), it's possible to do so, but it involves quite a bit of paperwork. The person who received the 1099-INT needs to file Form 1040 Schedule B and subtract the amount of interest that should "belong" to the other person as a "Nominee Distribution", and then issue their own 1099-INT to the other person for that amount of interest, so that the other person can appropriately list it on their own return. For details, see the section on "Nominee distributions" in Publication 550. I think the situation you describe is very similar to the Example listed there of an account shared between siblings with an agreement for 30% to go to the sister:
You and your sister have a joint savings account that paid $1,500 interest for 2016. Your sister deposited 30% of the funds in this account, and you and she have agreed to share the yearly interest income in proportion to the amount each of you has invested. Because your SSN was given to the bank, you received a Form 1099-INT for 2016 that includes the interest income earned belonging to your sister. This amount is $450, or 30% of the total interest of $1,500.
You must give your sister a Form 1099-INT by January 31, 2017, showing $450 of interest income she earned for 2016. You must also send a copy of the nominee Form 1099-INT, along with Form 1096, to the Internal Revenue Service Center by February 28, 2017 (March 31, 2017, if you file Form 1099-INT electronically). Show your own name, address, and SSN as that of the “Payer” on the Form 1099-INT. Show your sister's name, address, and SSN in the blocks provided for identification of the “Recipient.”
When you prepare your own federal income tax return, report the total amount of interest income, $1,500, on Schedule B (Form 1040A or 1040), Part I, line 1, and identify the name of the bank that paid this interest. Show the amount belonging to your sister, $450, as a subtraction from a subtotal of all interest on Schedule B (Form 1040A or 1040) and identify this subtraction as a “Nominee Distribution.” (Your sister will report the $450 of interest income on her own tax return, if she has to file a return, and identify you as the payer of that amount.)
Another option, if there's enough interest involved that the tax on it is worth keeping track of and so you want to split the interest income but not deal with quite as much paperwork, is just for the person who isn't issued the 1099-INT to give a "gift" each year to the person who is issued the 1099-INT for the amount of tax caused by their "share" of the interest. This probably works best for a fairly informal arrangement and if the people involved are in similar tax brackets.