What is the most common fruit related surname?

The problem with answering that question is that none of the fruit related surnames appear on lists of 'most popular surnames' or the name is a variation which doesn't resemble the common English language spelling of a fruit.

One might be 'Fig':

Recorded as Fig, Fige, Figg, the diminutives Figgen and Figgin, the prejoritives Figger and Figure, the patronymics Figgs, Figers, Figgers, Figgins, Figures, and others, this interesting surname has a number of possible origins. Firstly, it may derive from the German word "feige" meaning fig, and would have been a topographical name for someone who lived by a fig tree or a metonymic occupational name for a grower or seller of figs.

http://www.surnamedb.com/Surname/Figure

Berry seems to be non-fruit related:

This is an ancient English surname of topographic or locational origin. It derives either from the pre 7th century 'byrig', meaning 'a fortified place' or the later 'beri', or 'buri' denoting a fortified manor house. Topographically the surname was given either the owner of a manor house, or possibly to somebody who lived close by. Locationally the surname may derive from such places as Bury in Huntingdonshire, recorded as Byrig in the Anglo Saxon Chronicles of the year 974, Bury in Lancashire or Sussex, Berry(brow) in Yorkshire, or Bury St. Edmunds, Suffolk, this latter place being recorded as Sancte Eadmundes Byrig in 1038. The modern surname can be found as Berry, Berrey, Berrie, Bury and Burry.

http://www.surnamedb.com/Surname/Berry

'Cherry':

Recorded in the spellings of Cherry, Cherryman, and Cherriman, this is an English occupational surname. It originates from the old English word 'chirie' and it is either occupational and and as such describes a grower or seller of cherries, or it may have been a medieval nickname of endearment for somebody with rosy cheeks or even red hair. In the Middle Ages England experienced a warm climate period, as it had done in Roman times and is perhaps now in the 20th century. As a result certain fruits which had previously only been grown on the Continent were cultivated in parts of England, the cherry being a popular form.

http://www.surnamedb.com/Surname/Cherry

'Plum':

This interesting and unusual surname has two possible derivations. Firstly, it may be of Anglo-Saxon origin, as a topographical name for someone who lived by a plum tree, from the Olde English pre 7th Century word "plume", plum (tree). Alternatively, it may be of Old French origin, as a metonymic occupational name for a plumber, from the Old French "plomb", itself from the Latin "plumbum", meaning lead. This was later assimilated to the Old French "plummier", a plumber. Other variant spellings from this source include Plumb, Plumbe and Plum(p)tre(e). The surname itself is first recorded in the early 13th Century (see below), while one Simon Plumbe is mentioned in 1251, in Records of the Abbey of Ramsey (Huntingdonshire). John Ploumbe is noted in the Subsidy Rolls of Suffolk in 1327, and Ralph Ploome is listed in 1327 in the Subsidy Rolls of Derbyshire. A Coat of Arms was granted on June 10th 1563 to a family in Kent, depicts a black bend vair cotised on an ermine shield. Lendall Plome was christened on May 8th 1580 at St. Michael's, Cornhill, London, while John Plumb married Ann Gabrill on April 22nd 1664 at St. Paul's, Covent Garden, Westminster, London. The first recorded spelling of the family name is shown to be that of Geoffrey Plumbe, which was dated 1208, in the "Charter Rolls of Suffolk", during the reign of King John, known as "Lackland", 1199 - 1216. Surnames became necessary when governments introduced personal taxation. In England this was known as Poll Tax. Throughout the centuries, surnames in every country have continued to "develop" often leading to astonishing variants of the original spelling.

http://www.surnamedb.com/Surname/Plum

'Apple':

Recorded in several forms including Apple, Appel, Appoell, Epple, Eppel and possibly others, this is a surname of the British Isles. It may have two possible origins. The first is English, but from the pre 7th century Scandanavian word 'apaldr', meaning apple, and hence an occupational name for a grower of fruit, and specifically apples.

http://www.surnamedb.com/Surname/Apple

http://names.mongabay.com/most_common_surnames.htm

On this web site, 'Berry' ranks 168 and 'Cherry' ranks 780. Apple, Fig, Orange, Melon (or Mellon), Lime, and Lemon don't appear at all.

There is another web site that has some interesting name origins.

'Orange':

First found as a girl's name in medieval times, in the forms Orenge and Orengia. The etymology is uncertain, and may be after the place in France named Orange. This is a corruption of Arausio, the name of a Celtic water god whose name meant "temple (of the forehead)". Later it was conflated with the name of the fruit, which comes from the Sanskrit for "orange tree", naranga. The word was used to describe the fruit's colour in the 16th century.
Orange can be used as a surname, which may be derived from the medieval female name, or directly from the French place name. First used with the modern spelling in the 17th century, apparently due to William, Prince of Orange, who later became William III. His title is from the French place name.

http://www.behindthename.com/submit/name/orange

'Oliver'

From Olivier, a Norman French form of a Germanic name such as ALFHER or an Old Norse name such as Áleifr (see OLAF). The spelling was altered by association with Latin oliva "olive tree". In the Middle Ages the name became well-known in Western Europe because of the French epic 'La Chanson de Roland', in which Olivier was a friend and advisor of the hero Roland.
In England Oliver was a common medieval name, however it became rare after the 17th century because of the military commander Oliver Cromwell, who ruled the country following the civil war. The name was revived in the 19th century, perhaps in part due to the title character in Charles Dickens' novel 'Oliver Twist' (1838), which was about a poor orphan living on the streets of London.

http://www.behindthename.com/name/oliver

Recorded in over one hundred spelling forms including Oliver, Olivier, and Olver (English and Scottish), Olive, Olivier, Ollivier (French), Oliva, Olivo, Oliverio, Livieri, Uliveri, Veiri, Vieri, Vieiro (Italy), Olivas, Olivera (Spain & Portugal) and recorded throughout Europe in localised spellings, this is a surname of either Ancient Greek or Roman origins. However spelt it has always been symbolically associated with the olive tree and in particular as an original baptismal name, the olive branch, the emblem of peace. The name was popular throughout Europe in the pre Middle Ages, being borne as Oliverus by one of Emperor Charlemagne's knights, and a friend of Roland in the 9th century. The name as the baptismal "Oliverus" was recorded in the English Domesday Book of 1086, whilst perhaps surprisingly the first known recording as a surname in any spelling and in any country is that of Walter Olifer, a charter witness in Scotland in the year 1180. Other very early examples of the surname include Jordanus Oliueri, in the Pipe Rolls of Cornwall, England, in 1206, whilst John Oliver appears in the charters of Soltre Hospital, Scotland in 1250. Perhaps the most interesting nameholder was Lawrence Olivier, later Lord Olivier, 1906 - 1988, the world famous Shakespearean actor. Throughout the centuries, surnames in every country have continued to "develop" often leading to astonishing variants of the original spelling.

http://www.surnamedb.com/Surname/Oliver

'Vine'

Recorded in many spelling forms including Vine, Vigne, Vyner (England), Lavigne, Devigne, Desvignes, Vinau, Vigne, Vignaux, Vignault, (France), Vingneri, Vignolo, Vignozzi, Vignone (Italy), Vina and Vinas (Spain & Portugal), Wein, Weine, Weins and Weiner (Germany), and many others, this surname is of Roman (Latin) origins. Deriving from the ancient word 'vinum' meaning wine, and recorded in almost every European country in its myriad localised forms, it is either a topographical name for someone who lived at vineyard, or an occupational name for a vine producer, or it derives from the popular personal name of endearment of the pre 5th century a.d.'Vinea', which actually means "sweet wine". The Romans spread the art of wine growing throughout their empire, wines being grown in England for instance, as far north as Yorkshire, and there are several places named Vineyard in the counties of Essex and Cambridgeshire, which may be sources of the later surname.

http://www.surnamedb.com/Surname/Vine

Hey, check this out:

https://en.wikipedia.org/wiki/List_of_common_Chinese_surnames

The most common fruit related name on earth is 'Li' - it means 'plum'.