There is no way to change the original person associated with an intake event however if you intake a roaming or abandoned animal as a new Stray Intake, perhaps using the "Unknown Person" record, and then an owner is later identified, you'll want to retain this history by creating a person record for the pet's owner and then complete a Return to Owner Outcome for the animal.

In the event that the owner still cannot retrieve their pet and it will remain in your custody, you can then follow this with an Owner Surrender Intake to bring the animal back into your program using the known owner's record. 

If you do not want each Intake/Outcome event to count towards your reporting numbers twice, you can use a combination of Intake/Outcome Subtypes to record these events, for example:

1. Stray Intake from Unknown Person, Subtype = Found Roaming, configured to COUNT
2. Return to Owner Outcome to Known Person, Subtype = Owner Located/Surrendering, configured to NOT COUNT
3. Owner Surrender Intake from Known Person, Subtype = Cannot Afford, configured to NOT COUNT
4. Adoption Outcome to Known Person, Subtype = Onsite Adoption, configured to COUNT

You can read more about subtype configuration and how these affect your reporting here:Best practices for configuring Intake / Outcome Subtypes

Another example scenario can be found here:
Best practices for configuring Intake / Outcome SubtypesHow to Process Intakes for Court Cases, Seizures, etc.