I have it from the records at the JGLS that the Youngs were part of the Heron Family. A very old Roma family. They appeared to simply change name at some point for no apparent reason. I have been able to verify this as fact - via the census's so as you go further back in time, be aware that a name change to Heron/Herring/Hearn is possible.
Miller in the North is a Romany surname I have come across in my own family, so I think you can say that there is a very good chance your family were Roma.
Just as an example (and one that could be quite relevant if we could only get back far enough to uncover the truth!)
Here is an 1851 Census from Thorner Yorks
HO107/2352/308
Miller Young head/Widower/60 no occ listed b.Yorks
Sarah Young dtr/unmarried/32 no occ listed b.Yorks
significantly, they are with three other families, the family of:
Maria Boswell head/Widow/36 GIPSY b.Nfk
and that of
Robert Young head/Mar/27 no occ listed b.Barnsley Yorks and wife Eliza.
And also that of
William Young head/Mar/35 no occ listed b.Lancs with wife Ruth.
(there are other family members to these three on the census).
Miller Young is very evident on the Heron family Pedigree deposited with the JGLS by the Revd George Hall. Only his name was very clearly, Miller Heron.
Miller Heron was reputedly married to Winifred BOSWELL Which explains to me why Miller Young was travelling with a Maria Boswell, who would have been his relative.
The Robert Young named was actually Millers son (known as Perrun Heron on the Pedigree) who married Elizabeth Gray.
And the William Young listed was Millers son William nicknamed Taiso, who married Ruth/Rodi.
There is absolutely no doubt in my mind that this is indeed Miller Heron with his family.