The Texas Company switched to Texaco Inc. in the early 1960s. I believe this was the time they started using the circle R beneath the star as the trademark (was formerly Reg T.M.)
I've found Texaco lease signs in the wild that had another porcelain strip sign that says "Texaco Inc" which Texaco placed over "The Texas Company" on the original lease signage. Not even decals or stickers, a whole other porcelain sign... That's Texaco for you, exacting and extravagant with their imaging standards.
The best "Texas Company" signs have logos... Not super valuable but cool