The name Ashildr (or Áshildur in present day Icelandic) is a composite of the words "Ás", the singular form of Æsir (Norse mythology gods), and "Hildur", a word-turned-name which most commonly means female warrior, Valkyrie or warfare in broader terms. In essence, her name thus means War Lord, a name which has strong ties with the Whoniverse.
When working on the alien helmet, The Doctor says he is 'reversing the polarity of the neutron flow' - this was a favourite saying of the Third Doctor.
The alien "Odin" wears a helmet with one eye covered. This is similar to the actual myths about Odin, who plucked out one of his own eyes in exchange for a drink from the Well of Knowledge.
Brian Blessed was originally cast as Odin, but he was diagnosed with a heart condition after collapsing on stage during a performance of King Lear and was forced to withdraw. David Schofield took over the role.
Guest star Maisie Williams is best known for playing Arya Stark on Game of Thrones (2011). Her on-screen brother in that series was played by Richard Madden, who was the real-life boyfriend of Jenna Coleman.