Ha ha...first thing I thought of when I read title.
The OP didn't require a real name or a real word. Didn't say it had to be in a dictionary or what dictionary it had to be in.It's not even a word...
I think someone already listed the shortest word that fits the bill: "a". As in, this is a particularly easy game to play due to the lack of constraints beyond only listing two words/names. Starts and ends with the letter "a". So it's meets all requirements, no?abetalipoproteinenmia - longest word starting and ending with A
aha - tied for shortest word starting and ending with a, where a is not the only letter.