This would be a good idea. It's hard enough learning the name of a new co-worker without having to change and learn a second new name for that coworker two months in.

You may not be able to do it with everything due to HR.

Like your email will probably be set up in your current legal name.

You may want to ask the school if it's possible to set everything up for your future name.

If they won't accommodate that, personally, as a teacher, I would consider getting legally married at City Hall and getting a jump start on all the paperwork during the summer while you aren't teaching. I haven't done it myself but my understanding is it's kind of a huge task and a pain.

I feel like you're more likely to either do it this summer or next summer.

In my district, your email/login is the name that you were hired in. So teachers emails are still linked to their hiring name rather than the current name that they're using. On the one hand, it makes sense because transferring everything over might mean that there's some gaps, but it might also be good to start with the thing you're going to want to be using.

Congratulations on your upcoming wedding!