The full question was:
If in acts 7:38 Stephen called Israel the church, does that mean the church was in the Old Testament or should we just call ourselves Israel?
This question is presumably based on Acts 7:38 in the KJV:
This is he, that was in the church in the wilderness with the angel which spake to him in the mount Sina, and with our fathers: who received the lively oracles to give unto us (Acts 7:38, KJV)
Almost all other versions render that word “church” as “congregation”, “assembly” or a similar word. For example, consider Acts 7:38 in the ESV:
This is the one who was in the congregation in the wilderness with the angel who spoke to him at Mount Sinai, and with our fathers. He received living oracles to give to us. (Acts 7:38, ESV)
The reason it was translated “church” in the KJV was probably due to the rules laid down for translators, which included the rule “the old ecclesiastical words to be kept,” with the example of “church” instead of “congregation” (which Tyndale’s translation typically used).
So in Acts 7:38 the Israelites were just a large group of people, not “the church”. In the same way, when we encounter the word church in other parts of the New Testament, we need to consider whether it is just talking about a group of people or whether it has some other special meaning. I think talking about them as the church is unwise because it tends to make us think that the Israelites were organised similarly to us and that they faced similar issues to us, while this isn’t always true (and again, this can apply just as much to talking about the New Testament church).
Israel were God’s chosen nation, like we are God’s chosen people. However, there is the big difference that all Israelites were born into God’s nation and then automatically expected to follow God without any choice, while we have to make the choice to follow God and join his chosen people. We are told that the things in the Old Testament were written for our instruction, and so we do have to be able to draw lessons from the experiences of the nation of Israel, but to do that we need to understand both the similarities and the differences rather than blurring them together. We are indeed a part of spiritual Israel and heirs of Abraham like the people of Israel, but we have to be careful how far we take the comparison and what we derive from it.