when I use a <hr/> tag between two names the space between them increases slightly?

Answer 1

Not necessarily. It creates a line in the next ehmm line. Something like this:
_____________________
This line may be used to divide a page. In a previous question, someone described how to make this line dotted. I think that was @PK.

Answer 2

From W3C website :
"Changes in HTML5
Although previous versions of HTML defined the hr element only in presentational terms, the element has now been given the specific semantic purpose of representing a “paragraph-level thematic break”.
Details
Some examples of thematic breaks that can be marked up using the hr element include a scene change in a story, or a transition to another topic within a section of a reference book."

All hr attributes are made obsolete in HTML5. Use CSS instead to style, control margin, width etc..