Advice please

A quick look at my previous DP post will let you know how new I am with these things.
By the way, I followed the advice they gave me and I am pleased to say that Peter's computer is now connected to the Internet again, thank you, but now I have another problem.

I have a website, Peter built it for me based on & # 39; WordPress & # 39; and I loved keeping it running. Now I received an email on your computer from a company called & # 39; Namecheap & # 39; It says that the registration for my website will expire soon and invite him to renew it, but when I click on the link, it seems to me that they have their own website. doing some kind of work.

I had the impression that my website was hosted by a company called Galaxy Web Solutions, so my question is this.

If I do not renew with Namecheap or if your site does not appear again in time for my renewal. Will my website disappear forever?

Thank you.