If you mean the meta title, then I do not see why you would be penalized. You may lose some juice on the key words being replaced.
you can change as often as you can but it would be not good to your SERPs because the will affect your target keywords and backlinks. better stick with one key and aim for more competitiive word after you got good ranking.
Google won't penalize your site for changing the title. If you are changing the title to make it more keyword rich, it is not a problem. BTW, I have been using a plugin in my site which maintains the title for posts/page, home page, archive page, etc. When I updated the plugin, the new version removed all existing titles and I had no titles, descriptions for many months, as I haven't noticed it for long. It doesn't affected my site much. so nothing to worry.
Hi, In my own experiences, tweaking your homepage or inner page title tag would be a recommended SEO practice according to your keyword strategies and competition analyzing. all the best,
No I don't think that Google will penalize you because changing the title tags according to the keywords are SEO practice.
Google won't penalize your site when you change your title tags but it does affect your rankings. So it's better to not change your title tags too often.