in xslt2 you could use regular expressions, in 1.0  just some
combination of substring-before = and contains will work, depending on
what you cases are

contains(@name('Home::') might work, that would match lkjhllHome::as
well but if your input is in a regular form and you are just trying to
distinguish Home::foo Home::bar and Work:foo then it's enough
or
starts-with(substring-before(@name,'::'),'Home') is true for
Home::foo and HomeOffice::foo
or
substring-before(@name,'::')='Home'
or...

David