You can raise money for yourself, your groups, or other individuals or groups on the Action Network. As described here, the first time you add a recipient to a fundraising or ticketed event page you'll be asked to create and connect a WePay or Stripe account. With WePay, you must link your group to an individual WePay account connected to your Action Network account -- you'll log in with that account later to retrieve both donations to you as well as donations to your group (separated out in different buckets, of course). If you do not want to be the WePay account associated with that group's fundraising and you'd rather a different administrator handle that, have them create the fundraising or ticketed event page the first time and link to their account.
With Stripe, you can create an entirely separate account for each group, or have all money go into the same Stripe account with no way of telling which recipient is which.
You can also search for other individuals or groups who have set up their WePay or Stripe accounts using the bottom section of the fundraising or ticketed event recipient addition window. If a group or individual does not appear, they have not set up their WePay or Stripe account yet and thus are not eligible to receive funds.
Note: With WePay, you must enter bank details within 30 days, otherwise you won't be able to raise further money on your fundraising or ticketed event pages until you do. You also must have a US Social Security number or Tax ID number to raise money via WePay. Stripe asks you for these details up front, and is available in more countries and currencies.