Yates (and its many variations) is a very common name in the UK, and is generally held to mean a gatekeeper or someone who lived by a gate. It is from the same origin as Gates or Geats, the G & Y being variations of the same letter.
A family crest or heraldic arms only relates to specific person & (sometimes) their branch of a family it was granted to. It does not apply to the name itself.
If you can trace your ancestry to a person who was given a "grant of arms" then the College of Arms in London will be able to confirm the grant and may be able to provide information on the derivation of the particular crest/arms used.