Unfortunately, I couldn't find any information on a specific "Gamecocks Background Vector Vector Vector HD" in the provided search results. However, I can suggest some possible alternatives to achieve a similar effect.

You can use the @mapbox/vector-tile package to create vector tiles and then use Expo's built-in support for popular icon fonts (via @expo/vector-icons) to display the Gamecocks logo as an SVG icon.

Here's a brief snippet to get you started:

import React from 'react';
import { View, Image } from 'react-native';
import VectorTile from '@mapbox/vector-tile';

const GamecocksBackground = () => {
  return (
    <View>
      <VectorTile
        url="https://example.com/gamecocks-vector-tile.json"
        style={{ width: 300, height: 200 }}
      />
      <Image source={require('./gamecocks-icon.png')} style={{ width: 100, height: 100 }} />
    </View>
  );
};

Note that you'll need to replace the https://example.com/gamecocks-vector-tile.json URL with the actual URL of your vector tile and adjust the styles as needed.

Alternatively, you can use a library like geojson-vt to slice your GeoJSON data into vector tiles and then display them using Expo's vector tile support.