I know what I'm looking for, but I don't know what it's called (DIY)

I have cut a round hole in a garden table for an umbrella. I want to finish it off by putting something like this (photo below) in the hole to give it a bit more strength and make it look a bit nicer. These are the same thing one might use to put up shower curtain rail or a clothes rail inside a wardrobe, but if I search for either of those what I find is quite small with a hole half the size I need for my large umbrella. The hole I have cut is 8cm in diameter. I've been searching for "circular bracket". Does anyone know if there's a technical name for one of these things? Thanks.


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https://www.themetalstore.co.uk/products/tube-clamp-wall-plate?utm_source=google&utm_medium=product_feed&utm_campaign=products&gclid=Cj0KCQjwjer4BRCZARIsABK4QeX0PCk1gckowmHBToJJWo6M3F4jd1oWL63yyv0lfJysgZut2jENE-UaAnODEALw_wcB
https://www.amazon.co.uk/Diameter-Plastic-Ventilation-Ducting-Spigot/dp/B08461ZH3F/ref=sr_1_36?dchild=1&keywords=wall+plate+round&qid=1595619602&sr=8-36
I just need to find the goldilocks size.
https://www.jtmplumbing.co.uk/malleable-galvanised-pipe-fittings-brackets-c545/commercial-decorative-floor-flanges-c829/jtm-pipeline-decorative-malleable-iron-screwed-floor-flange-type-2-p24189/s33110