Is it significantly inappropriate to wear clothes bearing the name of University X, when working as an official employee at University Y?
There are definitely cases in which it would stand out as strange or inappropriate.  You should be careful in cases of a rivalry, since that may be viewed as a significant statement even if you meant nothing by it.  (I'm thinking of Harvard vs. Yale or Illinois vs. Iowa.  Athletic rivalries are particularly troublesome, since students may consider the clothing a sign of active support for the rival university.  No reasonable person could take offense, but not everyone is reasonable.)

It's also risky spending too much time wearing clothing emblazoned with a much more prestigious name than the university you are currently at.  You don't want to look like you are ostentatiously reminding everyone that you graduated from Harvard, unlike the riffraff around you.

I don't think either of these will be an issue for wearing a Dalhousie University hoodie at Nankai University.  If this were in the U.S. or Canada, I don't think it would be a problem at all: the worst case scenario is occasional good-natured teasing, and even that's far from certain.  However, I have no experience with how it might be viewed in China, so it's worth looking into that specifically if you have reason to fear the reactions might be different.