Then they said, “Come, let’s build a great city for ourselves with a tower that reaches into the sky. This will make us famous and keep us from being scattered all over the world.” (Genesis 11:4, NLT)
I will bless you and make you famous, and you will be a blessing to others. (Genesis 12:2, NLT)
Fame in and of itself is not bad. However, when we pursue fame, it can keep us from what God wants us to do (in the case of those at the Tower of Babel, it kept them from filling the earth [Genesis 9:1]).
When we pursue God and what he tells us to do, any fame he brings ultimately blesses others.
Do I want my end to be famous or to be a blessing? If I pursue the former, it stops with me and is only about me. If I pursue the latter, it may or may not come with fame, but whether it does or not, I will be a blessing.