Updating your Texas LLC's registered agent on the Comptroller's website doesn't change it with the Secretary of State. You need to file a separate form on the SOS website and pay a $15 fee to make it official.
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Here it asks you who your registered agent in office is. The registered agent that you originally filed with the state of Texas. If it has changed, you'll need to update it here, but then you'll also have to file it with the state of Texas directly. There's an actual form you need to fill out over there on their website that you would have to submit. If you have access to the SOS Direct system, that's the online system that the state of Texas has where you can file different forms, you would be able to change your registered agent there, and you would also have to pay a fee, which is $15. Plus credit card fees if you pay by a credit card. But when you update it here, just know it does not update over there in the Secretary of State system. You can update mailing addresses here on the Comptroller's website and it'll carry over to the State of Texas, but your registered agent and the address for your registered agent does not get transferred over to the State of Texas. So you would actually have to file that form on the Secretary of State's website and pay the fee in order to get that updated.