It's possible you're name is getting autocorrected.
Once place that might cause this is if you have this name (with the A) entered in Contacts.
This is even more important if you have the problem contact selected under Settings > Mail, Contacts, Calendars > My Info (in the Contacts settings). Also, for web forms, look under Settings > Safari > AutoFill. See if it is turned on, and what contact you have selected.
Or it could be that your name ending in an 'a' is a valid name or word, and the spelling dictionary is being helpful.
In iOS 9 you are supposed to be able to override autocorrect by making an entry in the Text Replacement list that Johanna mentioned. Add a new item, enter your name in the Phrase field, leave the Shortcut field blank.
I don't know if this works in earlier version of iOS. I only saw it explicitly mentioned in an article about iOS 9.
Or you could try what I do, and just turn autocorrect off. I'm a terrible speller, but I find I'm less embarrassed by my obvious spelling mistakes than the sometimes outlandish results that I get in autocorrect.
I do leave it on on my iPhone. The small keyboard makes correcting mistakes more of a chore, and the shortness of most messages make it less likely I won't notice bad autocorrects.