Unfortunately, for those folk for whom English isn't a mother tongue, life is tricky to say the least
It's nigh on impossible to generalize with the English language, and suspect it's the same with most tongues - but ...............….
in simple form, and for those words like …. make, take, hope, nose, bake, and haze, that do not possess suffixes such ….. ing, tion etc., then the possession of the final letter 'e' makes it necessary to pronounce the vowels 'a' and 'o' as long sounding vowels - and not as short vowels as in cat, mat, peg, top etc.
But the rules change for example, with words such as hoping' - which has the suffix 'ing', but lacks the 'e' but nonetheless must still be pronounced with a long vowel sound 'o' as we would if the 'ing' were not there. If you understand language construction, this is a logical point, since the word, and others of similar ilk, have only a single consonant 'p' - but if the word was spelt 'hopping' - with two peeeeeees, then the presence of the double p automatically tells us the first vowel must be pronounced as a short vowel (as in hopping up and down) - tapping, hitting etc.
Just to confuse us however, there are words such as Nazeing, where the presence of only a single middle consonant would normally tell us that pronunciation would be with a long vowel 'a' - and the letter 'e' would be superfluous - this is back to words like hoping, making, taking etc.
No 'e' is required for us to know that with a single middle consonant we must pronounce the vowel as a long sound.
The answer here is possibly that that Nazeing is not a naturally occurring word, and is contrived/made up, so I suppose you can use the spelling and pronunciation of your choice
I have known instances of the word 'glueing' spelt with an 'e', but most people would probably not do this.
I've just flicked through Geoffrey C. Timberlake's book on the Nazeing Glassworks, but have failed to see an explanation as to why the Company name was spelt the way it was/is.
For Walton-on-the-Naze, spelling is thus and Naze is always with a long vowel - a rural township in north east Essex - on the coast. Is this the location of your R. Lee?? - and yes, suspect that Naze in this instance is, as you suggest, a promontory or nose (sticks out).
all really just a case of semantics - am sure you knew all this, and just wanted to see some spilled ink