In the Hebrew culture, a name refers to more than what a person is called. Especially in a Biblical context, a name often describes the identity and essence of a person. The Bible is filled with different "names" of God in the Old Testament, but these names aren't simply titles to refer to God. These names describe the nature and essence of who God is. These names describe the attributes and unique characteristics of God. This is important to know since, when God is called a certain name in scripture, one must seek to know how He is revealing that characteristic in the scriptures.
For example, in Genesis 21:22-34 the Lord is called "El Olam," which means the "Everlasting God." Since God is called this name, one must seek to understand how God is demonstrating His everlasting attributes in the testimony. This portion of scripture can make it kind of difficult if one does not take into consideration the full context of God's promises to Abraham. Recall that in Genesis chapter 12, God made an everlasting promise to Abraham: to make him a great nation, to give him a land inheritance, and to bless all of the families of the world through him by Messiah. At this point in scripture, God had provided Abraham with an heir to his name in his son Isaac. In this way, God was working towards fulfilling His promise to make Abraham a great nation. The scriptures testify that Abraham had been living in the land that God had promised, but that the land was not yet given to Abraham. However, Genesis 21:22-34 is a testimony that shows God working towards the fulfillment of that promise, and Abraham's recognition of such work.
In Genesis 21:22-34 the Bible explains that two Philistine rulers named Abimelech and Phicol sought out to meet with Abraham shortly after Abraham and sent Hagar and Ishmael out of his home. The Bible explains that these Philistine authorities sought Abraham out in order to make a treaty with him. The scriptures explain that both Abimelech and Phicol recognized that the hand of God was upon Abraham and that Abraham was in good favor with God. Therefore, Abimelech and Phicol went to befriend Abraham in order to ensure that they were in good position with God. The Philistine leaders knew that they didn't want to offend Abraham and by extension offend God and so they made Abraham swear in an oath to live peacefully among them in their land.
Abraham agreed to form this treaty with them, but he had one gripe. Abraham informed Abimelech that some of the Philistine men had seized a well that Abraham was using at some point in time, and Abraham was offended by that. Abimelech emphatically apologized and assured Abraham that such seizure was done without his knowledge. Therefore, Abimelech was more than willing to give the well back to Abraham. The Bible reveals that Abraham recognized the hand of God in this work. The scriptures show that, because Abimelech was willing to give Abraham the well, Abraham sought to ratify the treaty with gifts and offerings. Genesis 21:22-34 shows that Abraham took sheep and cattle and gave them to Abimelech to show thanks. The Bible also explains that Abraham took seven ewe lambs and placed them to the side. Abimelech asked Abraham why he separated the ewe lambs and Abraham stated that Abimelech was to take the seven ewe lambs as a form of a witness that the well Abraham received was his since he dug it. In this way, the seven ewe lambs were a witness themselves of the land that Abraham received.
Abraham recognized the hand of God in this work. The scriptures testify that when Abimelech and Phicol went back home, Abraham worshiped the Lord in the place where his well was and called the Lord "the Everlasting God." God's everlasting attribute was demonstrated in that God was making slow, but progressive efforts to fulfill His everlasting promises. Though Abraham was living in land that was not his, the receipt of the well was a sign of God's faithfulness to give Abraham the land. Abimelech gave Abraham the well and the land surrounding it, and though it was only a small portion of the greater land inheritance, Abraham was encouraged to see that God was doing what He promised over 25 years prior. Abraham recognized that time was not a relevant factor in God's ability to fulfill His promises. God gave Abraham a son when Abraham was 100 years old. God gave Abraham a small portion of land 25 years after He promised, and even though the well was taken from Abraham, God was sure to eventually place it back into the hands of Abraham according to His will and timing.
Then, it is also good to recognize that lambs were the token of ratification of God's promises. It was the lambs that Abraham "set apart" or "sanctified" to serve as a "witness" of God's promises. This is a picture of the role of Jesus Christ as Messiah. God was working on the fulfillment of 2 of His 3 promises to Abraham. In the process of doing so, God provided a picture of how He would fulfill the 3rd part of that promise. The Lamb of God who takes away the sins of the world as Messiah would be the fulfillment of that third promise. Jesus would be "set apart" and "sanctified" as the Son of God in order to serve as a witness of God's promises, being the fulfillment of God's everlasting promises. Since Jesus died and rose again, Jesus' identity as the Lamb of God reveals that He is able to fulfill God's eternal promises because He shares the same everlasting nature of God, being El Olam in the flesh!