Not a lot.; is is essentially a contraction of agus. You can probably always change is (when it means "and", there is another "is" which is totally different) to agus, however, there are situations where it's more or less common to use is in place of agus. e.g. It's common to use it to link pairs of things.
Then you would always be called Oighrig, in English and Gaelic. No one would deliberately call you the translated name if you didn't want to be called it. Many people have English names on their birth certificates but are known by their Gaelic names. Others have Gaelic names on their birth certificates and are always known by that name. It's a personal preference, and your preference would always (I would hope) be respected :)