Yes, of course! Stripe is built to process payments for all types of activities or businesses, which includes individuals. When you activate your account, you should select that you are an Individual/Sole proprietor.
The same settings would apply if you are a Riding or a Saddle club secretary or if you take care of the entry fees for small shows, as you are acting on behalf of a group which is not a registered business, you are ultimately in control of all the details of this account.
These settings are very important as they will be used Stripe to identify you and validate your account to make sure your funds are secure. Over time you will be asked to refresh your documents, so please take note of any correspondence sent by Stripe, and remember if in doubt, login to your Stripe account directly rather than using a link provided on an email.
Stripe typically requires the following documents to verify your identity.
one which serves as Proof of Identity
one which serves as Proof of Home Address
Please see below an extract form Stripe's documentation:
"Stripe is required to collect, verify, and maintain identity information on the individuals associated with a Stripe account. These requirements come from our regulators and financial partners, and are intended to promote transparency and prevent individuals from using complex company structures to hide terrorist financing, money laundering, tax evasion, and other financial crimes.
If we are unable to verify your business and/or identity programmatically when you sign up for a Stripe account, Stripe might require a copy of a government-issued photo ID to verify the information manually. If this is the case, you will be notified to log into your Stripe Dashboard and use the notification prompt in the top right corner to upload your documentation."
The original link is here https://support.stripe.com/questions/passport-id-or-drivers-license-upload-requirement
And here are more details on what type of documents you can use https://support.stripe.com/questions/documents-for-identity-and-home-address-verification