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As long as the content is bringing you traffic and conversions, keep the content online. Maybe you could place a popup on the old content to explain to people that you have rebranded, just so they don't get confused.

Hi sdaily, I'd definitely keep the existing GA property so you can see the full history in that one property. That way, you'll still be able to compare y/y traffic, etc. With a new property, you'll be starting your data from scratch and comparing different date ranges will be more difficult. Just create an annotation so you can keep track of the changeover date. Cheers, David