The case of ICFAI vs ICAI had been won by ICFAI in the Supreme Court(May 2007, refer: https://www.hindu.com/2007/05/23/stories/2007052303381300.htm). Now there is no bar imposed by ICAI, as regards CFA.
However, its always better if u inform the instt, through the form no. 103, as mentioned by Rajat.
Note: The above applies to the CFA offered by ICFAI. Not to the CFA of USA.