Homologies and common ancestry?

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1) If organisms X and Y have a common ancestor, they will have homologous structures;
2) X and Y have homologous structures;
∴ X and Y have a common ancestor.

First, is this a strawman? If not, what kind of argument is this called?

It is somewhat of a strawman in that you are implying that homologies are the only presented evidence of common descent, and also that all scientific claims must be able to be expressed in valid formal logical form. Really, very, very few things can actually be "proven" in such a rigorous manner as you seem to be requesting, rather scientists look at the available data and try to figure out which explanation better accounts for this data. Very rarely do such explanations stand up to being expressed in the form of symbolic logic, and that is why scientific ideas are open to change, but that doesn't mean science is a load of bull.

If your question is specifically about the argument form you presented (p—>q, q, ∴p) that is invalid because it is the converse error. However, if you are attempting to cast doubt on ideas of common descent with this post, you are yourself committing a logical fallacy. Argumentum ad logicam.

Homologous structures can evolve independently to some extent.

Heat pits on snakes evolved independently in two separate species for example. There are many more examples.

Similar environments produce similar adaptations without common ancestor.

Yes, as Letum pointed out, there is also the issue of convergent evolution. We tend to use computational genetic analysis to sort out issues of interrelatedness nowadays.

Its called Modus Ponens

No. It's the formal fallacy "affirming the consequent". Let P be "X and Y have a common ancestor" and Q be "they have homologous structures". The argument takes the form:
1. P => Q
2. Q
∴ P

Yes this is a strawman.

The argument should, I think, be approached as establishing a posterior probability, ie given Q we can reason the probability of P is sufficiently high. It can be argued that the explanation P is the most likely given the evidence Q.