The default Frontpage is a view (
admin/structure/views/view/frontpage/edit) showing a waterfall of all content that is Published and "Promoted to the Frontpage". By default, the Frontpage view's Title is "none" while the HTML Title tag is "Home | MySite.com".
So you can change the
Title of the view there to e.g. "Start" and the HTML title will change to "Start | MySite.com".
If, instead of using the Frontpage view, you choose a node for your home page (e.g. "node/10 ), then you can name the page "Home" and the HTML title will become "Home | MySite.com".
If you don't want the title of the page showing up in the page's content area (but you do want it in the home page's HTML
title tag), you can hide the title block in
The Metatag module, along with Token, can also be used for this and general SEO enhancements, but you said you are trying to avoid that.