Many words start with "A" and end in "Y". Here are a few examples, but the exact number depends on what you consider a "word" (including proper nouns, slang, etc.):
* Amy
* Andy
* Abby
* Ashley
* Alany (less common)
* Aprily (a less common way to refer to April)
* Angely (a variant spelling)
And many more names and less common words fit this pattern.