I want to change the short civ name of the Viking Empire to "Scandinavia". How do I do it in a modular mod.

I think it should be enought to just replace the name the the Text\XML. These are kind of 'modular' by default - newer files will override older one if both have the same item.
If that not work redirect the name (TXT_KEY_Whatever) to a new text item within the module.

I made a text file called "New_CIV4GameText" with the following text.

<?xml version="1.0" encoding="ISO-8859-1"?>
<!-- Sid Meier's Civilization 4 Beyond the Sword -->
<!-- Modified by the Civ Gold Team -->
<!-- -->
<Civ4GameText xmlns="http://www.firaxis.com">
<TEXT>
<Tag>TXT_KEY_CIV_VIKING_SHORT_DESC</Tag>
<English>Scandinavia</English>
<French>
<Text>Vikings</Text>
<Gender>Male</Gender>
<Plural>1</Plural>
</French>
<German>
<Text>Skandinavien</Text>
<Gender>Neuter</Gender>
<Plural>0</Plural>
</German>
<Italian>
<Text>Scandinavia</Text>
<Gender>Female</Gender>
<Plural>0</Plural>
</Italian>
<Spanish>
<Text>Escandinavia</Text>
<Gender>Female</Gender>
<Plural>0</Plural>
</Spanish>
</TEXT>
</Civ4GameText>

Didn't work. What should I do?

Odd... Maybe because you did not name it [modulename]_Civ4GameText.xml so it wasn't recognized as part of the module ?

Make it TXT_KEY_CIV_SCANDINAVIA_DESC and redirect the tag to the new item in the CivilizationsInfos.XML

I don't want to change the name of the Viking Empire, just the short form (à la Civ III).

I tried the first thing you did.