The Northampton logo has an interesting approach, explained with this diagram from the corporate guidelines.
As you can see an attempt has been made to incorporate a few elements and meanings into the logo, it only really works if the letters function as letters first and foremost. Good idea to incorporate a graphic based obliquely on something important and relevant to the town, but trying to mangle the letters ‘n’ and ‘u’ into a pre-existing shape seems a step too far.
It could be that I’m staying up too late but I see a stylised rabbit somewhere in there. The badge shape is however, a nice variation on the traditional shield, and hints at what could be done with this logo. The ‘u’ shape makes the logo feel unresolved.
On the plus side, I Like the choice of optima as a clean and softer modern font. Tightly spaced but still managing to be fresh and open without trying too hard to be dynamic and aspirational. The decision to set it all in uppercase makes alignment easy negating any awkward whitespace within the word.