Yes you can change blog name before and after applying for adsense and it will not affect your AdSense account
Also you can write article while your site is in review for Google AdSense
But there are some things that you need to remember
Don't ever change the template of your website when it is under review for Google adSense otherwise it will create problems for you.
If your site is under review and if you changed the template or theme of your site during this time then Google will reject your AdSense application and it will show you an error of VALUABLE INVENTORY-Under Construction. Because by this act of yours Google thinks that your site is not completely build up and it is still under construction
If your site is Under review for Google Adsense then during this period of time do not edit or change html section of your website otherwise google will detect that your site is not complete yet and is still under construction and hence it will reject your AdSense application then you have apply again for Google AdSense
Don't add or remove widgets during the time when your site is under review for google AdSense because it is also a sign of under construction. You can add or remove them before or after AdSense approval
I have started a Series of Questions related to blogging and If you check the series it will clear most of your QUESTIONS related to Google AdSense, Blogging, SEO and much more