dynamically instead of a fixed value in persistance

You can go with universal persistence (have universal persistence configured for your virtual server) and use the following iRule:

when RULE_INIT {
    set static::dynamic_persist_timeout 600
}
when HTTP_REQUEST {
    set http_cookie_list [HTTP::cookie names]
    if { [lsearch -glob $http_cookie_list "*_SESSIONID_*"] >= 0 } {
        set http_cookie_name [lindex $http_cookie_list [lsearch -glob $http_cookie_list "*_SESSIONID_*"]]
        set http_cookie_value [HTTP::cookie value [lindex $http_cookie_list [lsearch -glob $http_cookie_list "*_SESSIONID_*"]]]
        log local0. "cookiematch=${http_cookie_name},cookievalue=${http_cookie_value}"
        persist uie "${http_cookie_name}:${http_cookie_value}"
    }
}
when HTTP_RESPONSE {
    set http_cookie_list [HTTP::cookie names]
    if { [lsearch -glob $http_cookie_list "*_SESSIONID_*"] >= 0 } {
        set http_cookie_name [lindex $http_cookie_list [lsearch -glob $http_cookie_list "*_SESSIONID_*"]]
        set http_cookie_value [HTTP::cookie value [lindex $http_cookie_list [lsearch -glob $http_cookie_list "*_SESSIONID_*"]]]
        log local0. "cookiematch=${http_cookie_name},cookievalue=${http_cookie_value}"
        persist add uie "${http_cookie_name}:${http_cookie_value}" ${static::dynamic_persist_timeout}
    }
}

I tested this one in my environment using another BIG-IPs virtual server as a server emulation:

when HTTP_REQUEST {
    set http_cookie_list [HTTP::cookie names]
    if { [lsearch -glob $http_cookie_list "*_SESSIONID_*"] >= 0 } {
        set http_cookie_name [lindex $http_cookie_list [lsearch -glob $http_cookie_list "*_SESSIONID_*"]]
        set http_cookie_value [HTTP::cookie value [lindex $http_cookie_list [lsearch -glob $http_cookie_list "*_SESSIONID_*"]]]
        log local0. "cookiematch=${http_cookie_name},cookievalue=${http_cookie_value}"
    } else {
        if { [info exists http_cookie_name] } {
            unset http_cookie_name
        }
        if { [info exists http_cookie_value] } {
            unset http_cookie_value
        }
        for { set i 0 } { $i < 3 } { incr i } {
            append http_cookie_name [lindex {A B C D E F G H I J K L M N O P Q R S T U V W Z Y Z} [expr int(rand()*26)]]
        }
        append http_cookie_name "_SESSIONID_"
        for { set i 0 } { $i < 6 } { incr i } {
            append http_cookie_name [lindex {0 1 2 3 4 5 6 7 8 9} [expr int(rand()*10)]]
        }
        append http_cookie_name "_"
        for { set i 0 } { $i < 8 } { incr i } {
            append http_cookie_name [lindex {A B C D E F G H I J K L M N O P Q R S T U V W Z Y Z 0 1 2 3 4 5 6 7 8 9} [expr int(rand()*36)]]
        }
        for { set i 0 } { $i < 16 } { incr i } {
            append http_cookie_value [lindex {a b c d e f g h i j k l m n o p q r s t u v w x y z 0 1 2 3 4 5 6 7 8 9} [expr int(rand()*36)]]
        }
        log local0. "cookiegenerator=${http_cookie_name},valuegenerator=${http_cookie_value}"
    }
    HTTP::respond 200 content "responder\r\n" noserver Connection Close Set-Cookie "${http_cookie_name}=${http_cookie_value}"
    return
}

You can monitor your persistence table on CLI of your device under test:

watch tmsh show ltm persist persist-records mode universal all-properties