The Many Names of Thumbelina

Her original name was Tommelise. Tommel is the Danish word for thumb. When Hans Christian Andersen made up this name, he was clearly  inspired by older folklore existing in Denmark and other countries. Just for context, Thumbelina appeared in 1835, twenty-three years after the Grimm brothers' first collection featuring Daumling, and eighteen years after the writer Rasmus Nyerup referenced a Danish folklore character named Svend Tommling.

Andersen is one of the most frequently translated fairy tale writers in the world, and for every translation of his work, there's another name for Tommelise. Here's a list:

Albanian:
Gishtëza (gisht = finger; Gishtëza translates literally as Thimble)
Armenian:
Matnačap'ikë or Matnachapik (մատ, mat = finger)
Basque:
Erpurutxo (erpuru = thumb)
Belarusian:
Цалёўка/Calioŭka (цалевы, calievy = inch)
Bengali:
খর্যকায়ার বিবব়ণ/Kharvakāyār vivaraṇa.

• Translated by Madhusudan Mukhopadhyaya as part of the Bengali Family Library in 1858. (Catalogue of the Library of the Indian Office.)

Bulgarian:
палечка/Palechka, Palečka (palets = thumb)
Burmese:
 မလက်ငယ် (Ma Let-Than/Miss Little Finger)
Catalan:
Ditona (dit = finger)

• Manent i Cisa, Maria. Ditona. 1985.

Patufeta (Patufet is a Thumbling of Catalan folklore)
Central Alaskan Yup'ik:
Kumluckaq

• Primary Eskimo Program, Bureau of Indian Affairs. Kumluc'kaq. 1959.

Chinese:
拇指姑娘 (Muzhǐ Gūniang, Thumb Girl)
Czech:
Malenka (málo = small, maličký = tiny)
Dutch:
Duimelijntje (duim = thumb)
English:
Little Thumb.

• Wehnert, Alfred. Andersen's Tales for Children. Bell and Daldy. 1861.

In Mary Howitt's in Wonderful Stories for Children (1846), the heroine went simply by Tommelise. 
Little Ellie 

• Boner, Charles. A Danish Story-book. 1846.

Little Totty (tot: small child)

• de Chatelain. Tales and Fairy Stories. 1852.

Little Maja

• The Child's Own Book. 1853.

Little Tiny

• Paull, H. P. Fairy tales of Andersen. 1867, 1872.

Thumbling

• Wonder Stories Told for Children. 1880.
• Ketchum, Agnes Taylor. Kindergarten Gems: A Collection of Stories and Rhymes for Little Folks. 1890.
  
• The Boston collection of kindergarten stories. 1898.
  

Thumbelina

• Dulcken, H. W. Fairy tales and stories. 1882.

Lizzie Thumb

• Siewers, Carl. Hans Andersen's Fairy Tales. 1900. At the end she receives the name May.

Thumbeline

• Jerrold, Walter. The True Annals of Fairyland in the Reign of King Oberon. 1902.

Little Maia 

• Lang, Andrew. The Olive Fairy Book. 1907.

Thumbykin 

• Favourite Fairy Tales. Illustrated by Helen Stratton. 1908.

Thumbelisa

• Fairy Tales from Hans Christian Andersen. 1914.

Inchelina

• Haugaard, Erik Christian. Hans Christian Andersen: The Complete Fairy Tales and Stories. 1974.

Estonian:
Pöial-Liisi (pöial = thumb)
Finnish:
Peukalo-Liisa (peukalo = thumb)
French: 
La Petite Poucette (pouce = thumb)
Poucelina
Poucette
​"Mam'zelle Tom Pouce" was used as the French title for the 1978 anime adaptation.
Galician: 
Polariza
Georgian: 
ნამცეცა (namts’ets’a, tiny)
German:
Däumelinchen (from Daumen, thumb), 
Däumeline
Greek:
Τοσοδούλα (Tosodoúla – probably derived from the Greek word for “tiny”)
Hebrew: 
אצבעונית (Etsbeonit. This translates literally to Foxglove, which in Hebrew is derived from the word for finger. Foxglove flowers are the right size to be worn on fingers.
Hungarian:
Hüvelyk Panna (huvelyk = Inch, Panna = nickname for Anna); 
Pöttöm Panna (pöttöm = tiny)
Italian:
Mignolina (from mignolo, Little Finger)
Pollicina (from pollice, thumb)
Icelandic:
Þumalína (þumalfingur = thumb)
Japanese: 
親指姫 - (Oyayubi-hime, Princess Thumb)
Korean:
엄지 공주 - (Eomji gongju, Thumb Princess)
Latvian:
Īkstīte (īkšķis = thumb)
Lithuanian:
Coliukė (Colis = Inch)
Romanian:
Degețica (Deget = finger)
Polish – (list and translations by Bogusława Sochańska)
Calineczka (Rygiel 1909, Cal = Inch)
Calinka (Little Inch Girl, Lewestam 1859)
Calóweczka (Little One-Inch Girlie, 1892)
Paluszka (Little Finger Girl, Młodnicka 1892)
Malutka (Little One, 1898)
Dziecię elfów (Elfin Child, Niewiadomska 1899)
Kruszynka (Little Moppet, Przemski 1938)
Palusia (Little Finger Girlie, Tarnowski 1938)
Odrobinka (Little Whit Girl, Zechenter 1946).

• Sochańska, Bogusława. “Was a New Polish Translation of Hans Christian Andersen’s Fairy Tales and Stories Necessary?”

Portuguese: 
Polegarzinha (polegar = thumb)
Russian: 
Дюймовочка / Dyuĭmovochka (Дюйм = Inch)
Лизок с вершок/Lizok-s-Vershok (a literal translation of Tommelise)
Крошка/Kroshka (tiny; A. Fedorov-Davydov)
Томмелиза/Tommeliza (S. Zaymovsky)
Лизо́к с ноготок/Lizok-s-nokotok (nokotok = nail)
Serbian: 
Палчица, Palčica (Палац, Palac = Thumb)
Slovak: 
Palculienka (palec = thumb)
Swedish: 
Tummelisa (tumme = thumb)
Spanish:
Pulgarcita
Pulgarcilla (pulgar = thumb)
Almendrita (little almond)
Chiquirritica

• El Tesoro de la Juventud. 1915.

Turkish – Parmak Kız (Finger Girl. Parmak Cocuk is Thumb Boy)
Vietnamese:
Cô bé tí hon (tiny little girl)
Tí hon ("tiny" – a name also used for the Grimms’ Thumbling).
Nàng Út or Nang ngón út (Miss Little Finger) is also translated as Thumbelina.
Welsh:
Bodlen (bawd = thumb)
West Frisian:
Tommelyske

Sources:
http://www.ebooklibrary.org/articles/thumbelina