Functionally there is no problem renaming it to .php. If the site is an existing one that has already achieved good search engine ranking, it could cause some problems with searches unless you set up some HTTP 301 redirects from the old file name to the new one.
Changing the web server to process all HTML files as PHP will avoid the need to rename files at the slight expense of a bit extra processing. Frankly though, unless this is a really heavily trafficked site, you'll probably never notice the difference on any pure HTML pages.