If I pair my watch to a new iPhone, will I still have all the same information?

Basically, theun pair process creates a backup of your watch to your iPhone, or, in other words to your iCloud account, since you'll keep the same watch and sync it to your new phone, you won't lose your activity information. You can actually see a part in the article that Chris0107 mentioned: "iCloud doesn't store your Activity Sharing data.", but don't worry, actually it saves your activity. You can confirm that here:

https://support.apple.com/en-us/HT204518

I suggest to create an iPhone backup before switching to your new iPhone so you can have all of your workouts there. Steps here: https://support.apple.com/en-us/HT203977 at the iCloud section.

I went thru this process about 6 or 7 months ago.. Here is what I did and I did not lose my data

How to pair your Apple Watch with a new iPhone - Apple Support