First things first, the eum in your sentence is unnecessary. In fact, using it places emphasis on the person you would be receiving:
Whoever comes to us, him we will receive.
The feeling that this gives off is that there is a question about whom you will receive, and so the answer is "whoever comes to us."
Second, grammatically your sentence is a future more vivid, except that it uses the future perfect, which emphasizes the protasis. How exactly the Latin sentence would be constructed depends on why you're saying it.
Quisquis ad nos veniat accipiamus. // Whoever should come, we would accept them.
I.e. It is our policy that we receive anyone who comes.
Quisquis ad nos veniet accipiemus. // Whoever comes to us, we will accept them.
I.e. Someone is definitely coming, and whoever it is, we will accept them.
Quisquis ad nos venerit accipiemus. // Whoever comes to us, we will accept them.
I.e. I swear someone is coming, and when they do, we will accept them!
Moreland and Fleischer (p. 38) explain the use of the future perfect here:
NOTE: Occasionally, when the speaker wishes the implications of the condition to be exceptionally emphatic, the future perfect is used in the protasis instead of the simple future.
In indirect discourse with a primary verb, Woodcock in his A New Latin Syntax lays out the changes nicely. I'll rewrite the sentences to fit yours.
Quisquis ad nos veniat accipiamus. → Dicit quisquis ad nos veniat accepturos esse.
Quisquis ad nos veniet accipiemus. → Dicit quisquis ad nos veniat accepturos esse.
Notice that the distinction between the two completely disappear in indirect discourse.
For your original example, Woodcock summarizes it nicely:
The future-perfect indicative is represented by the perfect or by the pluperfect subjunctive, according to the sequence.
Therefore we get:
Quisquis ad nos venerit accipiemus. → Dicit nos quisquis ad nos advenerit accepturos esse.
N.B. I replaced your putare with dicere because the choice of verb depends on what exactly you mean by "think", for which the Romans had many different words that were nigh synonymous, but not exactly so. In this case, putare, censere, opinari, and credere are close, but change the meaning ever so slightly. Dicere though keeps it fairly neutral.