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Different name on O'levels and other documents

Hello,
I have an issue with my name. I completed my O'levels then I started ACCA. I am an ACCA affiliate now. But during the studies of ACCA, I completely changed my name. ACCA accepted my new name. I got BSC Hons from Oxford Brookes as per new name in ACCA records. So my O'levels has old name. Can anyone please tell me that would it create any problem for me in immigration or study abroad process that different name on legal and other study documents than O'levels.
Name changing on O'levels is not possible as per the policy.
I think embassies and immigration authorities only consider the highest degree and won't bother about O'levels. is it right?