I think you might need to start earlier than medieval times, as there are a lot of little periods in between that could change your answers. One way to look at the history of animals and their presence among people could be the ancient roman mosaics that show dogs with collars and leashes. This would fall under animal husbandry and zoology of antiquarian dates. People recorded epitaphs as a eulogy to their pets and often named them and tied memories to those writings.

"Animal Husbandry across the Western Roman Empire: Changes and Continuities" by Valenzuela-Lamas, Silvia; Albarella, Umberto European journal of archaeology your best bet would starting from Rome and working your way down to your desired place. as names were a mixture of roman and local language and identifiers with practices or places. Dogs based on breed had selective practices and may have been more of an agriculture job, but medieval portraits support the idea that animal companionship was a well-practiced relationship. I would check out JSTOR and ARTs and PRactices journals and phrase questions to " Agricultural relationships with animals. "

Some starting sources.

"Animal Husbandry across the Western Roman Empire: Changes and Continuities" by Valenzuela-Lamas, Silvia ; Albarella, Umberto European journal of archaeology

there is also " Companion Animals and Us: Exploring the Relationships Between People and Pets "edited by Anthony L. Podberscek, Elizabeth S. Paul, James A. Serpell ...

I might look under archaeological, biology, and social cultures journals th Companion Animals ...Furac, Michael Journal of Value Inquiry, 2019, Vol.53 (1), p.155-163

I'm sticking with 15th/16th-century England, where you're in luck: there's a fifteenth-century manuscript called 'The Names of All Manner of Hounds' that gives over 1000 helpful suggestions for naming your dog. You've got sweet ideas like Pretiboy and Mouse and Trinket and Honydewe, warrior-y stuff like Corage and Champyn and Grimbolde, job descriptors like Go-bifore and Holdefaste and Bryngehome and Kilbucke (Deerkiller), eyebrow-raisers like Helpeles and Leper, and of course the ones that to our ears are totally baffling - Meyntenawnse? Snacke? Garlik? Druggeman? I personally like Havegoodday.

The full list is given in David Scott-Macnab's paper 'The Names of All Manner of Hounds: A Unique Inventory in a Fifteenth-Century Manuscript', but if you don't feel like signing up for access to the article, here's the list. Just as a bonus: Anne Boleyn's dog was named 'Purkoy', from the French pourquoi (Why?), because it was so curious.

On whether dogs were part of the family or working animals: just like today, you got both kinds. There's plenty of evidence of much-loved and pampered lapdogs. Chaucer mentions the Prioress's little dogs, richly fed with roast meat and cake, and there are medieval images of family pets being fed at table - scroll down here for a scene from the early 15th-century Tres Riches Heures du Duc de Berry where two tiny dogs are actually up on the table, while someone's feeding a greyhound on the floor - or hanging out in ladies' rooms. John Caius, in Of English Dogges (1576) describes women's lapdogs in much the same terms as critics talk about them today:

These are little and prettie, proper and fine, and sought out far and neere to satisfie the nice delicacie of daintie dames, and wanton womens willes; instruments of follie to plaie and dallie withal... These Sybariticall puppies, the smaller they be ... the better they are accepted, the more pleasure also they prouoke, as méet plaiefellowes for minsing mistresses to beare in their bosoms, to keepe companie withall in their chambers, to succour with sleepe in bed, and nourish with meat at boord, to lie in their laps, and licke their lips as they lie (like yoong Dianaes) in their wagons and coches.... this kind of people, who delight more in their dogs, that are depriued of all possibilitie of reason, than they doo in children that are capable of wisedome & iudgement. Yea, they oft feed them of the best, where the poore mans child at their doores can hardlie come by the woorst.

He does, however, admit that these dogs have their uses. Apparently snuggling them can cure illness:

we find that these litle doges are good to asswage the sicknesse of the stomacke being oftentimes therevnto applyed as a plaster preseruatiue, or borne in the bosom of the diseased and weake person, which effect is performed by theyr moderate heate. Moreouer the disease and sicknesse, chaungeth his place and entreth (though it be not precisely marcked) into the dogge...

And people bought their dogs fancy stuff then, too. Frederic Madden's 'Privy Purse Expenses of Princess Mary, Daughter of Henry VIII' lists her ornate dog collars and leashes (a lyame is a leash): 'A lyame of white silk with collar of white vellat embrawdered with perles, the swivell of silver... Dog collors of crymson vellat with VI lyhams of white leather.... A lieme of grene and white silke....Three lyames and colors with tirrett of silver and quilt.'

But there were also working dogs. Many were hunting dogs, which Caius categorises carefully, not by breed but by function - the ones that hunt by sight, that hunt by smell, that hunt game vs fowl, etc. (The bloudhounde has 'lippes of a large syze & eares of no small lenght', so they apparently haven't changed beyond recognition...) These were valuable dogs, treated with great care. In the early fifteenth century, Edward, Duke of York, wrote The Master of Game (mainly translated from an earlier French work by Gaston Phoebus), where he spends a lot of time talking about hunting dogs. He writes about them with great affection and respect ('A hound is of great understanding and of great knowledge, a hound hath great strength and great goodness, a hound is a wise beast and a kind'), and he goes into into a lot of detail about how hounds should be looked after - they should have a big kennel with good ventilation and 'a fair green, where the sun shineth all day from morning till eve' to run about in, and it should be kept warm in winter and cool in summer; they even get their own personal attendant, a small boy trained to look after all their needs and even sleep in with them at night.

A 1390 act forbade anyone from owning a hunting dog unless they had a landed income of at least 40 shillings a year - the logic was that otherwise the lower classes would be out poaching when they should have been at church. But there were plenty of other careers for dogs. Carole Rawcliffe, in 'Town Tykes and Butchers' Hounds: Urban Dogs at Work in the Later Middle Ages', describes dogs turning the spit on which meat was roasted, or acting as guide dogs, or doing tricks to earn money for their masters, or helping to drive livestock - or, of course, being guard dogs for homes, storehouses, and even London Bridge.

These lower-status dogs probably didn't receive the same degree of care as the hunting dogs and lapdogs, because their owners didn't have the same amount of money available for luxurious kennels and costly remedies. But, overall, it seems like our relationship with dogs hasn't changed quite as much as you might think in the last five or six centuries.