Your choice of Romanization will depend on your target audience. In my opinion, your absolute safest bet is to go with strict Hepburn style. If it's for Japanese people, feel free to use kunrei. This is what Japanese people learn when they are kids, and many write their names that way. They learn Hepburn in English classes in junior high school. If it's targeting an English-speaking audience, though, it would be a bit confusing for someone who isn't familiar with Japanese to see something like "tyûsyajyô."
While Hepburn is the standard, many Western publications use something based on it but that uses a few shortcuts when talking about Japanese places or people's names. For example, it's totally fine to write "Shinzo Abe" without any marking on the long vowel. Notice how places like Tokyo or Kyoto have English spellings that technically deviate from accepted romanization standards.
There are some other shortcuts that are frequently taken with names, for example writing something like Kenichi (which would be けにち) instead of Ken'ichi, which is the 'right' way to write けんいち as it avoids all ambiguity.
Romanization can be a tricky issue, and some people take it pretty seriously. Nevertheless, we frequently take shortcuts when writing, especially when such shortcuts help to obscure the finer details of Japanese phonology and orthography that might be confusing to people who do not speak Japanese. The more pedantic you anticipate your readers to be, the closer you should stick to some standard.
Last, especially with people, it's best to ensure that someone does not have a preferred way of writing their name that deviates from standards.