Is it good to use domain name with blogspot hosting platform

once our blog has regular platform we start to think of getting domain name , blogger allowes us to use our personal domain name with blogspot hosting as its free , it looks good.

so quesiton is if blog is popular and suddenly you change to domain name using blogspot as its free

how it will affect the blog popularity,traffic  or is it one has to start from scratch again ,

eg. if blog name is   xyz.blogspot .com now  the xyz has purchased domain name what he should do ?