Suhaib is the name of one of the Prophet's companions, Suhaib Ibn Sinan Ar-Rumi, Ar-Rumi being an ascription to the Romans. He sought Asylum in Makkah after being taken as a slave by the Byzantines.
When he heard the call of Allaah's Messenger, sall-Allaahu `alayhi wasallam, he pronounced his Islaam. He may Allaah be pleased with him, migrated to Madeenah after being held captive in his own home in Makkah. He traded all of his possessions and his abundance of wealth for the sake of being in Madeenah with Allaah's Messenger, sall-Allaahu `alayhi wasallam.
As for the name, it is said to connate to the colour red, reddish hair and/or reddish complexion. The Urdu name, Zohaib, which you may be familiar with is a variant of Suhaib.
Hope it helps.
Was-salaam