I think there's a pasuk that begins and ends with almost every letter combination, even though some aren't in the siddur.

I found a few options online for helping with pesukim for names that aren't in the siddur:

 1.  This website has a list of pesukim by first and last letter, including ones that aren't in the siddur:  https://web.archive.org/web/20140803215133/http://www.nifla-ot.co.il/articles/138.htm

 2. This website allows you to search for every pasuk in Tanach that begins and ends with the letters you select!  It's really an excellent tool. In order to use it replace the א in the search bar with the first letter in the name, and replace the ת with the last letter, and then click on the חפש (search) button.  If you need any more help with it, let me know.  http://162.243.116.217/tnk/find.php?q=%5E%D7%90.*%D7%AA%24

3. If neither of those has any pesukim for your name, another option is to use this website that a friend of mine (AvnerMil) wrote, which allows you to search for ראשי תיבות or סופי תיבות for your name and should find you an alternative option.  Instead of starting and ending with the first and last letter of your name, the pasuk will contain the letters of your name as the first letters of consecutive words, or the last letters of consecutive words within the line, which is also acceptable as far as I know.
http://secretorah.com/