This is not for everyone, but there are multiple ways to greet new followers and I will explain the methods I use, since I am yet to be partnered but love to make all my new members feel welcomed.
The first method is via my e-mail inbox. I link my follow notifications to my gmail, then keep the window open on a second monitor while I'm casting. When I see a new follow alert from gmail pop up, I can welcome the new follower.
The other method is a bit more flashy - a pop-up image welcoming the follower will come up on your OBS and can play a new follower sound. This can also be used for new subscribers as well (for partnered streamers)
I use twitch.tv/SubAlert for this (the download is in the profile description) - and I use the tutorial here for setting up the notification / custom graphics (chroma-key) and custom sounds for the alert. I used adobe photoshop for my graphic design work on my welcome image.
I hope this is helpful for anyone looking for a way to welcome new followers!