Send me your store URL and explain me more where exactly you want to add H1 tag on your store.
There is by default a H1 tag to logo in shopify. You can check it in header. liquid file.
As we all know H1 tags are very important for SEO because it helps your website rank better they tell both search engines and website visitors what the content of pages is all about. I think you don't have to code the <h1> yourself.