TX DBA filing at State vs County

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My question is specific to Texas since I assume the answer may differ from state to state. However, I would be interested how other states handle this as well.

I understand that a DBA can be filed at the State level (SOS) or County level. Is there anything preventing someone to file a DBA at the state level and then someone else filing the same assumed name at their local county level?

If not, would this cause a conflict? Which would take precedence, State or County DBA filing, or would both have legal rights to use the name in the local county?