Sorry you are having this issue, I have a couple ideas on how we might be able to remedy this.
Could you share screen shots on how you have "Enable custom title" set up in the first and second app? Or a gif of the set up and the tab name not changing?
My first guess would be to use a separate variable and have the custom title be assigned to that variable. Potentially making a distinction between having a differently named variable in each app to avoid confusion.
As setting it to a more dynamic value in a query result might require you to re-run the query or not have a value if the query does not run when expected.
Or even hard coding the values if there are only a few options. But if you need to be dynamic then we just need to make sure the value given to "Enable custom title" is updating properly.
I just did some testing and I was able to get the tab name to change from a hard coded variable to the current users name.
Let me know if you are able to replicate the behavior as shown in the gif above