Yes, there was controversy, both in the general public and in the Nation of Islam. Muhammad Ali was not the first name that he was given upon conversion. After defeating Sonny Liston for the championship, he was given the name Cassius X to let go of his "slave name." It was just 10 days later that Elijah Muhammad saw an opportunity for promoting the Nation of Islam and gave Cassius X the new name, Muhammad Ali.
This was controversial in the Nation of Islam as members were not supposed to receive their original (Arabic) name until the return of the founder of the Nation of Islam, Master Wallace Fard. Even Malcolm X had not received his name. It was viewed that Ali was getting preferential treatment due to his stature.
It was also controversial among the general population. Harry Markson, the director of Madison Square Garden refused to introduce Ali by his new name at a fight saying, "we’ve made so much progress in eliminating color barriers, that it’s a pity we’re now facing such a problem, the heavyweight champion of the world preaching a hate religion.” All-time great heavyweight Joe Louis said of the change, "Clay will earn the public's hatred because of his connections with the Black Muslims. The things they preach are the opposite of what we believe."
Sources: Redemption Song: Muhammad Ali and the Spirit of the Sixties by Mike Marqusee
Harry Markson, 92, Colorful Boxing Director. Gerald Eskenazi. New York Times. November 12, 1998.
I was looking for specific comments about the name change itself but what I found was more along the lines of questioning the entire conversion to Islam and his motives. For example, this article quotes an earlier Saturday Evening Post article by Myrion Cope called "Muslim Champ" where he says:
Having succeeded Malcolm X as the loudest [sic] Black Muslim, Clay has been fighting a socio-religious battle with the Christian world, and this, more than anything else, seems to have taken away his former exuberance. He still acts the clown for TV cameras but only to sell fight tickets.
Later in that article, Cope calls Islam a cult and it seems that at least some people saw it as a publicity stunt. When I read Cope's words (especially compared to the quotes he uses from Ali), there's this racial tension to it. He doesn't seem to like the fact that Ali is loud, abrasive and unwilling to conform to any one sort of stereotype which Cope tries to shoehorn him into. He tries to make him a zealot for the religion when the very words he quotes from Ali make him out to be a pragmatic person trying to make sense of turbulent times.
Specifically about the name change (although this is more about Ali aligning himself with the more radical Nation of Islam), Martin Luthor King Jr said: "When Cassius Clay joined the Black Muslims and started calling himself Cassius X, he became a champion of racial segregation." This gets into issues regarding the direction of the civil rights movement (Nonviolence or any means necessary) which is sort of outside of the scope of your question, but Ali aligning himself with the certainly does seem to have caused ripples in the boxing and African american community.
I type this as I look at my Ali poster. He was a larger than life man with a ton of impact in his time. It's a shame his disease robbed him of so much.
Watch this: http://www.pbs.org/independentlens/trials-of-muhammad-ali/
Short answer is yes and it haunted him pretty much his whole career and beyond.
His momma named him Clay, I'm going to call him Clay.