I hope you know that HCs can be named by yourself.
It can be called London, Edinburgh, York, Manchester, or even Paris, Atlantis, Asteroid B-612, as long as you want.
Although it has nothing to do with the name of the city (it can be renamed anyway), if there is a second HC to switch, it would have to be completely different art and mods to show the appearance of different cities and to satisfy the desire to collect custom decorations. Birmingham is a great fit for the default name of the British second HC due to its massive urban growth ans expansion through a thriving industry during the AoE3 time frame.