I often wondered if Lamar didn't like the thought of the Chiefs name also because it was opposite of the Cowboys...cowboys vs indians so to speak.
He couldn't keep the Texan name obviously when moving the Chiefs to KC in 63. The NFL told him no to a franchise in Dallas, somewhat shunning him since the same year they said yes to other businessmen, founding the Cowboys. Another factor is the opposition/controversy between the NFL and AFL from the get go of Lamar founding the AFL. Possibly there was a rivalry between he and the Dallas businessmen who founded the Cowboys the NFL said yes too.
I dunno, all speculation on my part...but I have wondered if there was anything to a cowboys vs indians in Lamar's thoughts when he incorporated the indian theme.