Missing middle name in BRP applying for ILR from Tier 2 gene

Hi

I have been in the UK for 5 years on tier 2 general visa (renewed once at year 3). I got BRP rather than visa at renewal of tier 2 visa. I travel frequently out of country for work and used the BRP at least 15 times while leaving and entering country without a problem. Recently I went for LIUK test and they didn't let me sit the exam as BRP doesn't have middle name while my passport and name I registered for exam has middle name. My name is too long and many a times people miss my middle name and I thought my BRP doesn't have middle name because they don't have space on card or they typically don't include it so never bothered. After LIUK incidence I went back to my communications with home office and I see that the biometric appointment letter and some other home office correspondence I had included my full name including middle. I am sure I included my middle name whenever asked in all my applications. I am now applying for ILR but worried that they may reject it based on this name discrepnacy. I don't want to pay ILR fees again as I did for LIUK test becuase ILR is expensive. I have followed other threads in this forum and found some discussion but not final answer from anyone. Someone else had same problem but he never came back reproting how he resolved the issue or indeed there is no need to worry about it. Please advice.

Many thanks