It's possible to open a Personal Account in your name, you would need to link and confirm both a bank account and credit card so the account is "verified". If your account is unverified, you can still receive money but, you may experience holds and/or reviews on your funds - typically from 1 day up to 21 days. Also, there are limits on unverified accounts when it comes to both sending and withdrawing funds.
As a group or organization, your other option is a Business Account however, it still has to be in one person's name and you still want to ensure that it's "verified". One nice advantage of the Business Account is that you can display your group or organization's name or logo on the PayPal Screens and receipts and invoices. If you use a Personal Account, then people would see your email address and name - just something to consider.
