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Well, I wouldn't consider it 'correct' for the Flemish name, as its original pronunciation is obviously a different one, but when you say that 'there's no English name for it as there is for Brugge', you have just given an 'English' name for it that your colleagues use to make life easier for themselves--and it is also the French name: Zeebruges (https://en.wikipedia.org/wiki/Zeebrugge), and the 'English' name for Brugge is undoubtedly derived from the French name analogously. I'm sure they must have heard it pronounced [zeːˈbrʏɣə], but have clearly decided to use the easier option.
All you need for there to be a new name is really for someone to invent one. If I decide to call Zeebrugge 'Woppadoodle', I've just made up a new name that then exists, although of course it won't be in general circulation and few people other than me would accept it.
Fear not, once we have a 'Brexit', nobody will need to communicate with Zeebrugge any more, so the problem will resolve itself.
A section of my department at work communicates frequently with contacts in Zeebrugge. This section pronounces it 'Zea-brooj' as you would for Bruges. There's some logic here as I understand Zeebrugge is the port of Bruges, but as far as I am aware there's no English name for it as there is for Brugge. Is there any truth that pronouncing it 'Zea-brooj' is acceptable?