Shared Field Name Between Entity Types? I have always separated my field names by entity. e.g. 

field_paragraph_h2 or field_content_h2, 

but when you look at config, fields are designated by their entity type as well.

field.field.paragraph.paragraph_type.field_paragraph_h2 or field.field.node.content_type.field_content_h2

Am I safe using just field_h2 for both entity type field names, or are there instances with Drupal where this may be problematic?

e.g.

field.field.paragraph.paragraph_type.field_h2 or field.field.node.content_type.field_h2
You are safe to use the same name. The fields are unique for each entity type, even when they have the same name.

They have their own field storage configuration, instances and will be stored to dedicated database tables per entity type.