Google helps webmasters to show their profile name and photo on their website with rel= author markup verification method.
To verify rel= author markup you need to first contribute your website in your google+ profile, to do this first edit your profile and under contribute section add your website.
Now add the following link in your website
<link href='https://plus.google.com/u/0/+yourid' rel='publisher'/>
<link href='https://plus.google.com/u/0/+yourid' rel='me'/>
to do this go to blogger>> Edit HTML>> and under <head> add the code below to it
example :
<head>
<link href='https://plus.google.com/u/0/+yourid' rel='publisher'/>
<link href='https://plus.google.com/u/0/+yourid' rel='me'/>
now go to structural data testing and test for your site... congrats! you now verified your markup data.
<link href='https://plus.google.com/u/0/+yourid' rel='me'/>
now go to structural data testing and test for your site... congrats! you now verified your markup data.