"his newfound prominance" probably refers to the fact that Obama became very important (prominant) when he was inaugarated as the President of the US. (but could also refer to any time when he gained in popularity; I would need more context to be sure) "build a larger brand" means that Obama wanted to make even a bigger name for himself , which would certainly prove lucrative for him and his staff (for instance, he could capitalize on his popularity by giving speeches, opening conferencies etc).
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