[Rivkin]

Fugh, I'm not an expert on turkology, so it can all be bs, but:

AFAIK tamga is usually just a signature. Turkish writing evolved from hieroglaphic to alphabet based, and so did the tamgas. There are 3 types of tamgas - consisting of one symbol (Type I). Usually these are the old ones, correspond to pictogramms or hieroglyphs. Very often have a totemic (or animistic) symbolism.Type II - tamgas consisting of two symbols that are symmetric or anti-symmetric to each other. These tamgas usually have to be understood as a combination of individual characters forming a word (with some of the vowels, especially initial vowels omitted). Why turks specifically liked symmetric writings (like swastika - two letters "a") I don't think anyone knows. The third type is tamgas composed of completely different letters, again these are already writing using an alphabet.

Concerning the first sword - these symbols can be tamga, or they can be not, I don't know. However in turkish alphabet this lazy n is usually "t" (however sometimes m or if looked from a different agnle -o and dz can be written quite similarly). Example - attached is an example from Karachai (turkish tribe from northern Caucasus).

Conerning the second sword - that's a classical tamga, probably modified Type II (symmetric with respect to one axis, anti-symmetric with respect to another). The letters involved seem to be "a or ae" and "n".

I'm not an expert in tatar to know which word exactly they coded like this...
Concerning family names - nothing comes up immediately, unfortunately because the letters are very popular ones, there are dozens of tamgas that use at least one of these letters + something else - for example a circassian tamga on the second picture, but did not yet find something exactly like this.