Davenport was one of the earliest surnames in Britain. The name dates back to the time of the conquest of William I. William the Conquerer strengthened the power of his crown by building castles and giving the confiscated land of rebels to his followers.

Generally speaking, however, the cross is associated with the Christian faith. Coat of arms shields were recorded in words, rarely pictured in old documents. There are few colors used in heraldry.

http://www.college-of-arms.gov.uk/faq.htm

A. No. There is no such thing as a 'coat of arms for a surname'. Many people of the same surname will often be entitled to completely different coats of arms, and many of that surname will be entitled to no coat of arms. Coats of arms belong to individuals. For any person to have a right to a coat of arms they must either have had it granted to them or be descended in the legitimate male line from a person to whom arms were granted or confirmed in the past.

John Scott Davenport JSDDOC@aol.com

I'm no expert on Heraldry, but I believe that all members of provable
descent from an ennobled ancestor were/are entitled to use the Coat of Arms,
which was/is designed and approved by the College of Heraldry in London.
Without the College, there would have been chaos relative to Coats of Arms,
no rules of design, no protection of designs, and indiscriminate usage, etc.
All of which nevertheless exist today among hucksters of one kind or another.
Coffee mugs emblazoned with a Coat of Arms of some design alleged to belong
to your surname are the rage at the moment.
Those royally empowered to use one of the four versions of the
Davenport Coat of Arms approved by the College of Heraldry, which exists
today purely for antiquity worship, historical color and ego trips, were/are
those who can trace back, legitimately or illegitimately, to the titled
ancestor. Originally only the heir-at-law-eldest, most direct male had the
title and the Coat of Arms, but that has long gone by the wayside. In later
centuries family member of titled lines and lesser status used it with
impunity. Acknowledged or proven bastards of titled ancestry could use the
Coat as long as a black bar was imposed diagonally across the design. This
was known as the "Bar Sinister" and was worn with pride by some.
There is a formal nomenclature relative to what a Coat of Arms must
contain in terms of elements and design integrity. Frankly, today anyone who
wants to use a Coat of Arms, official or one of their own making, can do so.
But there is enough snobbery and family pride left among British nobility,
although they no longer have any power other than ceremonial, that the
College of Heraldry continues to thrive, being supported in part by the
Crown, Parliament, and the Nobility as one of Great Britain's many attractive
tourist traps. I understand that most of the College's income today is
derived from Americans with delusions of grandeur.
Those traditionally entitled to use one of the four versions of the
Official Davenport Court or Arms are identified in "Burke's Peerage," the
blue book of British Royalty, which like the "World Almanac" is revised and
issued every year. A copy of "Burke's Peerage" costs around $750, the last I
heard twenty years ago. (It's not something that I consider one of life's
necessities.) Public Libraries in metropolitan centers generally have back
editions, donated for in-kind tax credits, in most instances, from wealthy
patrons. The LDS Family History Library in Salt Lake City has microfilm
copies of most of the editions, going back to the beginning, 1815 if I recall
correctly, and missing only a few years.
There are several on the DAVENPORT-L Rootsweb subscriber list who
likely can do a better job about this than I can. But as long as you asked,
that's the extent of my knowledge. Hope it helps.
John Scott Davenport
Holmdel, NJ