Yes. The options are:
If the child can write their name and sign the signature card, the account can be opened in the child's name and under their Social Security number with a parent(s) or guardian as the joint owner.
If the child is too young to write their name, then the account can be opened in an adult's name with a title "For Benefit Of the child's name".
Another option if the child is too young to write their name and the account needs to be in the child's name and under their Social Security number for tax purposes, an Illinois Uniform Transfer to Minor Act account can be opened by an adult, who would be the custodian of the account. Specific rules apply to these types of accounts and should be reviewed to make sure the custodian is willing to follow the rules.