Names That Mean Seventh

The short form Shira is more manageable. 

Bathshira

Name for a seventh child, back when people had them. 

Septima

Septimus is one of the more dashing of the birth-order Latin number names that were revived by the Victorians. So even if you don't anticipate son number 7, you might be bold enough to consider this relic, certainly preferable to sixth-son name Sextus.
 Septimus was popularized by the Roman Emperor Septimus Severus, a patron of arts and letters. There was a Septimus in Wilkie Collins's The Moonstone, in Dickens's The Mystery of Edwin Drood, and in Trollope's Barchester novels. Probably it is most familiar to modern readers as one of the principal characters in Virginia Woolf's Mrs. Dalloway, and as Harry Potter wizard, Septimus Weasley. There is also Septimus Heap, a series of bestselling fantasy novels by Angie Sage.

Names That Mean Seventh

The names

Bathshira

Septima

Septimus