Married surname or first name on ILR but Maiden Surname on Passport

[MuhammadM86]

Dear All

Not sure if I should post this post into another location, if so sorry and kindly move it to the relevant area.

Has anyone have this situation, their life in the UK is in their married surname or even first name (i.e. EUSS, ILR, Driving Licence, banks etc and their passport is in their Maiden name due to national country refusing to change the name.

I would genuinely appreciate your input if someone is in the same situation and how is it perceived and dealt with at immigration, i.e. when entering and leaving the country? Is it simple and you just show Marriage Certificate or more complicated or not accepted at all?

Thanks in advance.