Is there a name for the phobia of not having access to the internet?

Nomophobia is the fear of being out of mobile phone contact.

Is there a name for the fear or phobia of being away from / not being able to reach the internet?

There isn't a word for precisely this fear (yet), but if you want a fancy-sounding neologism, here is fear of away from Internet in transliterated Greek: macriapodiadictuophobia.

If you apply the same technique in Latin, the result would be abinterretemetus.

(In case you're wondering about good ole English, it turns out that it's much more ghastly: awayfrominternetfear.)

However, if you could use words that connote more of an addiction to the internet, then the answers to this question may suffice: cybernaut, nethead, and netizen. Most macriapodiadictuophobes are netheads, and vice versa.

Fear of the internet would be interretephobia, so perhaps fear of being away from it would be abinterretephobia.

Well, the word is 'discomgoogolation.'

Check Collins Dictionary:

Discomgoogolation: a feeling of anxiety felt by someone who is unable to access the internet

Note that the word is informal.