I also thank my partner, Alex, who has always been by my side through thick and thin. I also thank my partner, Alex, who is by my side through thick and thin. Both are not too formal, nor too casual. Both are fine. Added the full stop on the end. . I would not write I would like to thank my partner, Alex, who has always been on my side. As this implies sides and conflict, rather than companionship, support directly. . Personally I'd go with the present tense version. It's a little more interesting. The past one has more of a sense of history together, which is good, but brings in a sense of past, so the future is yet to be seen. . BTW: always "rain or shine", never the other way round, unless you are trying to be different.

As a native speaker, it's more common to say, read, and hear: I would like to thank my partner Alex, who has always been by my side through thick and thin. And I don't feel that "thick and thin" is too casual in this case because book dedications are very personal and provide a sentiment that is very genuine. They are formal yet heartfelt from the author. Hope that makes sense. Best wishes :)

thank you Aneli and Josephine

I would like to thank Alex ( use conditional it seems more professional) who has always been by my side ( use present perfect to emphasise that he was with you in the past and that he still is now). 😇

It should be: I would like to thank my partner, Alex, who has always been on my side.