That's the low-cost option. When I had my cat cremated I opted for private cremation where each pet gets their own vessel in the crematory. (There can still be a tiny bit of ash mingling, as sometimes air currents will carry some flakes into adjacent vessels.)

https://thepetlosscenter.com/our-locations/austin/

She was with me almost 20 years, and it was worth the extra cost to be able to have a remembrance of her.

That's the standard (cheaper) approach, but you can also pay a little more to have your pet cremated alone and get their ashes. My wife works in the funeral industry and she's done this with all of her pets that she's lost.