I now use the new Space Marine rules for my Chapter so that they are their own.
I no longer utilize the rules for the Salamanders Space Marine Chapter for my guys.
As for their specific traits, I could not decide on any particular one.
I instead gave them the following advantages and drawbacks:
    Cleanse and Purify     ---     Take the Fight to Them
    We Stand Alone         ---     Eye To Eye
I chose the first advantage because not only did I have lots of assault weapons for my Marines, I also like the fact that it keeps them moving with a decent amount of fire power. With a plasma rifle and a melta gun in each ten man squad, this makes them a mid range match for almost any target.
The second advantage helps out the close combat aspect for my Marines. I have axes for all their close combat weapons, a task that took a while to model. I also have each ten man squad in a Rhino and with two flamers. This makes them very mobile with an added punch to soften up enemies right before an assault.
The minor drawback is not only used for the rules requirement, but it also helps out in the back story about my Chapter. The fact that they are entirely alone without support, or so it seems, makes tham more mysterious and stalwart.
The major drawback is just like the minor one. Since my Chapter hails from an earlier time, they have a smaller amount of advanced vechiles and craft. I choose to have only a Landspeeder Squadron, armed with Multi-Meltas. This makes them pretty nice, fast moving tank hunters are always a pain to any enemy force. Also, it brings out a more foot soldier quality to my Chapter.
But as for the names for my units, as the title of the page suggests, I gave a special name as well as an individual glyph for each type of squad. I did this to be different and to give my Chapter its own identity.
Each unit type bears its glyph in their left shoulder pad or fuselage. On the right side, all marines and vechiles bear the Glyph of the Iron Mountain, shown below. This helps bring them together, yet still allows distinction.