这个句子中有两个重要的知识点:
一是made a name for himself = become famous，如:
They soon made quite a name for themselves as pop singers.
二是 come to = get to 渐渐的, come to be known 渐渐被人所熟知，如:
I come to be known to my students. I got to know him.
[一] come to知识拓展: come to短语拓展本文主要就知识点二
come to 进行拓展学习
(1) come to 后接名词、数词、代词或不接任何，意指，谈到，涉及到:
When it comes to physics, he is a complete stranger. 谈到物理他完全是个外行。
(2) 表示“合计，总共”，同amount to:
How much does the bill come to？帐单上共多少钱？
(3) 表示“开始……所认识，被……所记起。”突然想起（无被动式):
In a flash, the truth came to him. 突然间，他明白了真相。
(4) 发生(在某人身上), 降临于(某人):
Happiness will come to you as long as you are after it. 只要你追寻它幸福会降临于你。
(5) 恢复知觉，苏醒过来:
After three hours in the hospital bed, he began to come to. 躺在医院床上三个小时后, 他开始苏醒过来。
(6) come to a(n)... end 有⋯⋯结果( 结局、下场):
Those who has done evil things will come to no good end.做坏事的人不会有好下场。
(7) come to life 活跃起来 come to light 被发现, 被大家知道:
(8) come to nothing / no good 没有结果/成就 :
(9) come to oneself 恢复知觉, 恢复正常
(10) come to sb.’s attention / notice 受到某人注意
(11)come to the point 谈正题, 谈主要问题
(12)常见“come to a 名词”结构表示达到……状态/结果的习惯用语：Come to decision…达成决议
come to an agreement / understanding / terms.. 谅解，协议，或和解
come to a halt 意为“停止
come to an end 结束
come to a conclusion 得出结论；结束；告终
come to a head 达到危急的关头
come to an agreement 达成协议
come to a stop 刹车；停下
come to a close 渐进结束
come to a decision 作出决定
come to a finish 结束；完成
come to a settlement 解决；和解
come to an understanding 议定；商定
come to a standstill 停住；停滞不前
come to a climax 达到高潮
come to a period 结束；告终
come to an arrangement 谈妥；达成协议
come to a compromise 达成妥协
come to a stand 停顿
[二] come to知识拓展二
A. came to be known 渐渐被知晓/称作
come/get 动词不定式结构 表示一种情况的变化过程，表示出“逐渐”的含义。在汉语译文中，有时并不一定译出来，如：
(1) She will come to be ashamed of what she has done today.总有一天她会为她今日的所作所为而感到羞愧。
(2) Soon they’re getting to have a better understanding of the problem.
他们对这一问题逐渐有了较深的理解。
总结: come to 后接名词、数词、代词或不接任何词，主要意指，谈到，涉及到，有结果，开始认识等。come/get 动词不定式结构 表示一种情况的变化过程，表示出“逐渐”的含义。
