Lodger contract and council tax

Hello
I will soon apply for an ILR, I am currently under a tier2 visa, and I am worried about my housing situation. I have a tenancy agreement with my landlord, but none of the bills are under my name. The house is registered for council tax and bills under his name. And I pay the bills directly to him. I am sure he does pay them and there is no problem with that. However my name does not appear on bills, besides internet bills and my bank statements. Would that hurt my application for ILR or any visa extensions I would ask for? Meaning home office will find my name appearing for income taxes but not with council tax services. I ve been in this situation since 9 months now, but I did not mind then because I have been told council tax is a property tax and not a person tax. My landlord would like to change our tenancy agreement to a lodger contract from now on. Again, would that hurt anyhow my applications for ILR?

Thanks for your help, I am very stressed about this..

You are overthinking. It is not an issue. There is no law that you MUST be on bills and council tax bill.

There is no requirement to submit address proof for ILR.

I thought I might be over thinking, but it's true I have no clue how these things work. I am really worried they ll think I was not in the country or I was scamming council tax as I won't appear in the council tax records.

If you are living with landlord then you will need lodger agreement because Assured tenancy cannot exist where landlord is also living under same roof.