I am having the home title issue as well.
My title is showing up on the homepage for other installs of WP (older versions) that have WordPress / Yoast SEO installed but after trying to use the plugin on the latest version of WP, the title tag shows on the homepage in my browser, but not in Google. All other pages work, but not the home page.
Rather than being:
"Dog Training California - Expert Dog Trainers - Dog Training"
It is showing in Google as:
"Dog Training California" and thats it.
Im thinking its an issue with latest WP compatibility or something...
After updating a lot of my sites to latest WP I am finding that the home title is changing on all of them to just the first 3 words instead of the full title of the homepage.
Any fixes or suggestions?