DNA in genealogy surname Bay

[Bay89]

Yes I'm definitely trying to connect my Bay family line to one of the Bay Lines I've traced in the UK maybe you can hopefully find the coat laof arms.
Attached is the ship list

[Bay89]

Full list

[Bay89]

It is the end of the day and the brain is not working at peak, but here are a few thoughts.

Do you know who else was on board the ship and where they came from? Did they all have the same set of political or religious beliefs, e.g., Puritans, Royalists, etc? Could either aspect narrow down John's origin in the British Isles?

Was John Bay traveling with anyone? I guess 16 wouldn't have seemed as young back than as now, but it seems young to be traveling by himself. If not, was he part of the crew?

Would someone from Glasgow or Dublin have to go to Gravesend to leave for the American colonies back then, or were there closer ports?  Since he left from Gravesend, are the probabilities higher that your ancestor was from London?

Dumb but basic question: were the "way back" matches on men also named Bay/Bayes, etc? Our surname matches a few that are different, even though it was a y-DNA test.

And you might be into the realm of history rather than genealogy. I mean you might need to look for references in literature, historical writings, etc., for men named Bay in London, Dublin, and Glasgow. Court records? Parliamentary records? I don't know what is available.

Leaving at age 16, you probably wouldn't find John himself, but maybe a trace of the family. Any indication of their economic or social state?

Has anyone done a one name study of Bay?

from what I have read there were a few ways someone at the age of sixteen could find themselves indentured in the colony. Typically not by choice.
Do you think John Bay was living in greater London, possibly his parents had died. John now an orphan on the streets of London or perhaps a town near Gravesend or in Gravesend its self, easily found himself subject to forced indentured? I've read even ship masters forced many into indentured servitude apon arrival to the Colonies the ship masters sold them for profit.

[Ruskie]

Who knows. Your scenario may be right.

What leads you to believe that John is entitled to a Coat of Arms?

Added: I see from the transcription above, that his forename is “Jo” .... Are you sure his name is John, or could it be Joseph, or Jonathan? 

Added: A google search throws up quite a bit of information related to John Graunt. I am currently on my ipad so searching is a bit tricky, but it seems there was quite a trade in transporting servants from London to America, so it may be that that is John’s reason for going to America. Seems it was slavery of sorts: http://www.rootschat.com/links/01nae/ (from what you wrote it seems you probably already know that).

[Bay89]

I only assumed that he was entitled a Coat Of Arms, based of off what I've researched and read especially in Sir Thomas Banks work "Extinct and Dormant Peerages of England". Also reading about the lineage of The Barony of Bayeux and The Viscounts of Bay. The word Bayeux became Bay when the English language became dominant over Latin and French.

Originating from an Ancient Norse bloodline that married into an ancient Celtic Breton bloodline in the British Isles: the daughter of Alan De Lincoln and the daughter of Robert De Romilly. In the 1100s AD.

There's considerable pedigrees and Coats of Arms for the family spelling its name Bay as derived from Bayeux. Known in the beginning of the Feudal period in Great Britain (12th century) as the Barons De Bayeux.

There are separate Coats of Arms for
Ranulf VII and his decendants:
Bay of Bradden
Bay of Berkshire

Also granted Coats of Arms were the lineage of a Bay family: Earls of Chester  and William De Bay Lord of Copeland.
Cadet branches of the family
Bay of Dorsetshire

Suspirius De Bay II of Clapham and Aylesthorpe.

Robert De Bay of Bradwell

Sir Thomas De Bay, Knight
 Ikham, Kent (died 1339)

Bay of Careby

Bay of Lynwood

Robert de Bay of Bradwell

Bay of Somerset

Bay of Yorkshire

Bay of Tealby

Bay of Covington

But my ancestral composition of my DNA points to ancient Western Scotland or Ireland. Most likely the Very ancient sea-kingdom of Dalraida. The Kingdom of Dalriada included Western Scotland and Northern Ireland. I don't know. I guess my goal here at the moment is trying to connect my oldest known direct paternal ancestor to one of these specific and separate Bay Family lineages.

[Bay89]

Who knows. Your scenario may be right.

What leads you to believe that John is entitled to a Coat of Arms?

Added: I see from the transcription above, that his forename is “Jo” .... Are you sure his name is John, or could it be Joseph, or Jonathan? 

Added: A google search throws up quite a bit of information related to John Graunt. I am currently on my ipad so searching is a bit tricky, but it seems there was quite a trade in transporting servants from London to America, so it may be that that is John’s reason for going to America. Seems it was slavery of sorts: http://www.rootschat.com/links/01nae/ (from what you wrote it seems you probably already know that).

I came across a John Graunt as well. It ended up up being a different John Graunt.
The John graunt who was Merchant and shipmaster out of London master of the ship 'Safety' died the same year he arrived to Norfolk Virginia colony with my ancestor John Bay 1635 there was some sort of a sickness going around and several ship captains passed away upon arrival to the colonies that same year.

[KGarrad]

I can't comment on the DNA aspect, as I won't have anything to do with DNA!

As for heraldry: a coat-of-arms is granted to a named individual.
The arms are thereafter passed on through the male line; sometimes differenced if more than 1 son.

There is no such thing as a "family" coat-of-arms!

It is usual to start with yourself, and work backwards through the generations.
If, and when, you come across a person entitled to a coat-of-arms, then, and only then, can you possibly claim to be able to use of the arms.

In early heraldic history people claimed use of a coat-of-arms by continuous use.
But the Heralds Visitations were intended to stop this use (or misuse!).

[Ruskie]

Possibly also a co-incidence of similar surnames? There may have been many other Bay (and variant) families but there is only surviving documentation about, or mentions of, the prominent ones, who you may, or may not, be descended from. 

Do any of your DNA matches also have the surname Bay by any chance? What level do they match with you eg at 67 markers? 12 markers?

Have you considered contacting other men with the Bay surname to see if they would be willing to take a Y-DNA test, so you could compare results?