You could overwrite the value of the parameter by using a simple script that emits a "set parameter" service message.
By using a dedicated service message in your build script, you can dynamically update build parameters of the build right from a build step (...)
With that approach, here are the steps that you need to perform:
In the first build config, define a custom build parameter and set its value to the unique number you're generating. Do this directly from the script that generates the unique number by writing something like this to STDOUT:
##teamcity[setParameter name='magicNumber' value='1234']
In the dependent build config, you now have access to that parameter. Using a second build script, you can overwrite the teamcity.build.branch
with the same mechanism:
##teamcity[setParameter name='teamcity.build.branch' value='the new value']
Note 1: I recommend against overwriting the built-in parameters, because this might have strange side-effects. Rather, define a custom parameter in the second build config and use that for your visualization purposes.
Note 2: In case you decide to ignore Note 1, it may be necessary to overwrite the build parameters by setting the dependency property as outlined in the docs in section "Overriding Dependencies Properties":
##teamcity[setParameter name='reverse.dep.*.teamcity.build.branch' value='the new value']